Balaji Class 10 Maths Solutions Chapter 10 Trigonometrical Ratios and Identities Ex 10.1

Balaji Class 10 Maths Solutions Chapter 10 Trigonometrical Ratios and Identities Ex 10.1 त्रिकोणमितीय अनुपात एवं असमिकाएँ

Ex 10.1 Trigonometrical Ratios and Identities अतिलघु उत्तरीय प्रश्न (Very Short Answer Type Questions)

प्रश्न 1.
यदि sinθ = [latex]\frac{3}{5}[/latex], तब tanθ का मान ज्ञात कीजिए।
हलः
Balaji Class 10 Maths Solutions Chapter 10 Trigonometrical Ratios and Identities Ex 10.1 1
Balaji Class 10 Maths Solutions Chapter 10 Trigonometrical Ratios and Identities Ex 10.1 2
पाइथागोरस प्रमेय से, (कर्ण)2 = (लम्ब)2 + (आधार)2
(5)2 = (3)2 + (UPBoardSolutions.com) (आधार)2
25 = 9 + (आधार)2
25 – 9 = (आधार)2
16 = (आधार)2
[latex] \sqrt{{16}} [/latex] = आधार
4 = आधार
Balaji Class 10 Maths Solutions Chapter 10 Trigonometrical Ratios and Identities Ex 10.1 9

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प्रश्न 2.
यदि cosθ = [latex]\frac{1}{3}[/latex], तब sinθ का मान ज्ञात कीजिए।
हलः
Balaji Class 10 Maths Solutions Chapter 10 Trigonometrical Ratios and Identities Ex 10.1 5

Balaji Class 10 Maths Solutions Chapter 10 Trigonometrical Ratios and Identities Ex 10.1 4
पाइथागोरस प्रमेय से, (कर्ण)2 = (लम्ब)2 + (आधार)2
(3)2 = (लम्ब)2 + (1)2
9 = (लम्ब)2 + 1
9 – 1 = (लम्ब)2
8 = (लम्ब)2
Balaji Class 10 Maths Solutions Chapter 10 Trigonometrical Ratios and Identities Ex 10.1 6

प्रश्न 3.
यदि costθ = [latex]\frac{4}{5}[/latex], तब tanθ का मान ज्ञात कीजिए।
हलः
Balaji Class 10 Maths Solutions Chapter 10 Trigonometrical Ratios and Identities Ex 10.1 7
Balaji Class 10 Maths Solutions Chapter 10 Trigonometrical Ratios and Identities Ex 10.1 5
पाइथागोरस प्रमेय से, (कर्ण)2 = (लम्ब)2 + (आधार)2
(5)2 = (लम्ब)2 + (4)
25 = (लम्ब)2 + 16
25 – 16 = (UPBoardSolutions.com) (लम्ब)2
9 = (लम्ब)2
∴ लम्ब = [latex] \sqrt{{9}} [/latex] = 3
Balaji Class 10 Maths Solutions Chapter 10 Trigonometrical Ratios and Identities Ex 10.1 3

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प्रश्न 4.
यदि secθ = 2, तब [email protected] का मान ज्ञात कीजिए।
हलः
Balaji Class 10 Maths Solutions Chapter 10 Trigonometrical Ratios and Identities Ex 10.1 10
Balaji Class 10 Maths Solutions Chapter 10 Trigonometrical Ratios and Identities Ex 10.1 11
पाइथागोरस प्रमेय से, (कर्ण)2 = (लम्ब)2 + (आधार)2
(2)2 = (लम्ब)2 + (1)2
4 = (लम्ब)2 + 1
4 – 1 = (लम्ब)2
3 = (लम्ब)2
∴ लम्ब = [latex] \sqrt{{3}} [/latex]
Balaji Class 10 Maths Solutions Chapter 10 Trigonometrical Ratios and Identities Ex 10.1 12

प्रश्न 5.
यदि tanθ = [latex]\frac{1}{\sqrt{3}}[/latex], तब [latex]\frac{2 \tan \theta}{1-\tan ^{2} \theta}[/latex] का मान ज्ञात कीजिए।
हलः
∵ tanθ = [latex]\frac{1}{\sqrt{3}}[/latex]
Balaji Class 10 Maths Solutions Chapter 10 Trigonometrical Ratios and Identities Ex 10.1 13

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प्रश्न 6.
यदि sinθ = [latex]\frac{4}{5}[/latex], तब 3 secθ – 5 cosθ का मान ज्ञात कीजिए।
हलः
Balaji Class 10 Maths Solutions Chapter 10 Trigonometrical Ratios and Identities Ex 10.1 14
Balaji Class 10 Maths Solutions Chapter 10 Trigonometrical Ratios and Identities Ex 10.1 15

Ex 10.1 Trigonometrical Ratios and Identities लघु उत्तरीय प्रश्न (Short Answer Type Questions)

प्रश्न 7.
यदि [email protected] = 3, तब सिद्ध कीजिए कि : [latex]\frac{4 \sin \theta+3 \cos \theta}{8 \sin \theta+5 \cos \theta}=\frac{6}{11}[/latex]
हलः
Balaji Class 10 Maths Solutions Chapter 10 Trigonometrical Ratios and Identities Ex 10.1 16
Balaji Class 10 Maths Solutions Chapter 10 Trigonometrical Ratios and Identities Ex 10.1 17

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प्रश्न 8.
यदि cosθ = [latex]\frac{\sqrt{3}}{2}[/latex], तब सिद्ध कीजिए कि 4 cos3θ – 3 cosθ = 0
हलः
Balaji Class 10 Maths Solutions Chapter 10 Trigonometrical Ratios and Identities Ex 10.1 18

प्रश्न 9.
यदि tanθ = [latex] \sqrt{{2}} [/latex] -1, तब सिद्ध कीजिए कि cotθ = [latex] \sqrt{{2}} [/latex] + 1
हलः
Balaji Class 10 Maths Solutions Chapter 10 Trigonometrical Ratios and Identities Ex 10.1 19

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प्रश्न 10.
यदि cosθ = [latex]\frac{4}{5}[/latex], तब सिद्ध कीजिए कि [latex]\frac{\tan \theta}{1+\tan ^{2} \theta}=\frac{\sin \theta}{\sec \theta}[/latex]
हलः
Balaji Class 10 Maths Solutions Chapter 10 Trigonometrical Ratios and Identities Ex 10.1 20
Balaji Class 10 Maths Solutions Chapter 10 Trigonometrical Ratios and Identities Ex 10.1 21

प्रश्न 11.
यदि sinθ = [latex]\frac{\sqrt{3}}{2}[/latex], तब सिद्ध कीजिए कि 4 cos3θ – 3 cosθ = -1
हल:
Balaji Class 10 Maths Solutions Chapter 10 Trigonometrical Ratios and Identities Ex 10.1 22

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प्रश्न 12.
यदि tanθ = 2, तब सिद्ध कीजिए कि secθ sinθ + tan2θ – cosec2θ = [latex]\frac{19}{4}[/latex]
हल:
Balaji Class 10 Maths Solutions Chapter 10 Trigonometrical Ratios and Identities Ex 10.1 23
Balaji Class 10 Maths Solutions Chapter 10 Trigonometrical Ratios and Identities Ex 10.1 24

Ex 10.1 Trigonometrical Ratios and Identities दीर्घ उत्तरीय प्रश्न (Long Answer Type Questions)

प्रश्न 13.
यदि sinθ = [latex]\frac{a}{b}[/latex], तब सिद्ध कीजिए कि (tanθ – cotθ) = [latex]\frac{2 a^{2}-b^{2}}{a \sqrt{b^{2}-a^{2}}}[/latex].
हलः
Balaji Class 10 Maths Solutions Chapter 10 Trigonometrical Ratios and Identities Ex 10.1 25

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प्रश्न 14.
यदि cotθ = [latex]\frac{3}{4}[/latex], तब सिद्ध कीजिए कि [latex]\frac{\sin \theta+\cos \theta}{\sin \theta-\cos \theta}[/latex] = 7
हल:
Balaji Class 10 Maths Solutions Chapter 10 Trigonometrical Ratios and Identities Ex 10.1 26

प्रश्न 15.
यदि tanθ = [latex]\frac{a}{b}[/latex], तब सिद्ध कीजिए कि [latex]\frac{a \sin \theta-b \cos \theta}{a \sin \theta+b \cos \theta}=\frac{a^{2}-b^{2}}{a^{2}+b^{2}}[/latex]
हल:
Balaji Class 10 Maths Solutions Chapter 10 Trigonometrical Ratios and Identities Ex 10.1 27

प्रश्न 16.
यदि tanθ = [latex]\frac{4}{3}[/latex], तब सिद्ध कीजिए कि [latex]\sqrt{\frac{1+\sin \theta}{1-\sin \theta}}[/latex] = 3
हलः
Balaji Class 10 Maths Solutions Chapter 10 Trigonometrical Ratios and Identities Ex 10.1 28

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प्रश्न 17.
यदि costθ = [latex]\frac{5}{13}[/latex], तब सिद्ध कीजिए कि [latex]\frac{2 \sin \theta-3 \cos \theta}{4 \sin \theta-9 \cos \theta}[/latex] = 3
हलः
Balaji Class 10 Maths Solutions Chapter 10 Trigonometrical Ratios and Identities Ex 10.1 29
Balaji Class 10 Maths Solutions Chapter 10 Trigonometrical Ratios and Identities Ex 10.1 30

प्रश्न 18.
यदि sinθ = [latex]\frac{4}{5}[/latex], तब सिद्ध कीजिए कि [latex]\frac{4 \tan \theta-5 \cos \theta}{\sec \theta+\cot \theta}=\frac{28}{29}[/latex]
हलः
Balaji Class 10 Maths Solutions Chapter 10 Trigonometrical Ratios and Identities Ex 10.1 31
Balaji Class 10 Maths Solutions Chapter 10 Trigonometrical Ratios and Identities Ex 10.1 32

UP Board Solutions

प्रश्न 19.
यदि tanθ = [latex] \sqrt{{2}} [/latex] – 1, तब सिद्ध कीजिए कि sinθ cosθ = [latex]\frac{\sqrt{2}}{4}[/latex]
हलः
Balaji Class 10 Maths Solutions Chapter 10 Trigonometrical Ratios and Identities Ex 10.1 33

UP Board Solutions

प्रश्न 20.
यदि cosecθ = [latex]\frac{5}{3}[/latex], तब सिद्ध कीजिए कि [latex]\frac{\cos \theta-\frac{1}{\tan \theta}}{2 \cot \theta}=-\frac{1}{5}[/latex]
हलः
Balaji Class 10 Maths Solutions Chapter 10 Trigonometrical Ratios and Identities Ex 10.1 34
Balaji Class 10 Maths Solutions Chapter 10 Trigonometrical Ratios and Identities Ex 10.1 35

Balaji Publications Mathematics Class 10 Solutions

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