# Class 10 – Introduction to Trigonometry – Previous years Questions

Introduction to Trigonometry – Previous years Questions

1. The value of θ for which cos(10° + θ) = sin 30° , is
1. 50°
2. 40°
3. 80°
4. 20° [CBSE 2020] [1 Mark]
2. The value of θ for which sin (44° + θ) = cos 30° , is
1. 46°
2. 60°
3. 16°
4. 90° [CBSE 2020] [1 Mark]
3. If tan A = 1, then 2 sin A cos A = ________. [CBSE 2020] [1 Mark]
4. What is the value of (cos2 67° – sin2 23°)? [CBSE 2018] [1 Mark]
5. In figure, PS = 3 cm, QS = 4 cm, ∠PRQ = θ, ∠PSQ = 90° , PQ RQ and RQ = 9 cm. Evaluate tan θ. [CBSE 2019] [1 Mark]
6. If tan α = 5/12, find the value of sec α. [CBSE 2019] [1 Mark]
7. Evaluate:
$\left&space;(&space;\frac{sin&space;47^{\circ}}{cos&space;43^{\circ}}&space;\right&space;)^{2}&space;+&space;\left&space;(&space;\frac{cos&space;30^{\circ}}{cot&space;30^{\circ}}&space;\right&space;)^{2}&space;-&space;\left&space;(&space;sin&space;60^{\circ}&space;\right&space;)^{2}$ [CBSE 2020] [2 Marks]
8. Evaluate:
$\frac{2&space;sin&space;68^{\circ}}{cos&space;22^{\circ}}&space;-&space;\frac{2&space;cot&space;15^{\circ}}{tan&space;75^{\circ}}&space;-&space;3&space;tan&space;40^{\circ}&space;tan&space;45^{\circ}&space;tan&space;50^{\circ}$ [CBSE 2020] [2 Marks]
9. If 4 tan θ = 3, evaluate
$\frac{4&space;sin&space;\theta&space;-&space;cos&space;\theta&space;+&space;1}{4&space;sin&space;\theta&space;+&space;cos&space;\theta&space;-&space;1}$. [CBSE 2018] [3 Marks]
10. If tan 2A = cot(A -18°), where 2A is an acute angle, find the value of A. [CBSE 2018] [3 Marks]
11. A, B and C are interior angles of a triangle ABC. Show that
1. $sin&space;\frac{B&space;+&space;C}{2}&space;=&space;cos&space;\frac{A}{2}$
2. If ∠A = 90°, then find the value of tan$\frac{B&space;+&space;C}{2}$. [CBSE 2019] [3 Marks]
12. If tan (A+B) = 1 and tan (A-B) = 1/√3, 0° < A+B < 90°, A>B, then find the value of A and B. [CBSE 2019] [3 Marks]
13. Prove that :
$\frac{sin&space;\theta&space;-&space;cos&space;\theta&space;+&space;1}{cos&space;\theta&space;+&space;sin&space;\theta&space;-1}&space;=&space;\frac{1}{sec&space;\theta&space;-&space;tan&space;\theta&space;}$ [CBSE 2020] [3 Marks]
14. Prove that
$\frac{sin&space;A&space;-&space;2&space;sin^{3}A}{2&space;cos^{3}A&space;-&space;cos&space;A}&space;=&space;tan&space;A$. [CBSE 2018] [4 Marks]
15. If 1+sin2 θ = 3sin θ cos θ, then prove that tan θ = 1 or tan θ = 1/2. [CBSE 2019] [4 Marks]
16. Prove the following:
$\frac{1}{1&space;+&space;sin^{2}\theta&space;}&space;+&space;\frac{1}{1&space;+&space;cos^{2}\theta&space;}&space;+&space;\frac{1}{1&space;+&space;sec^{2}\theta&space;}&space;+&space;\frac{1}{1&space;+&space;cosec^{2}\theta&space;}&space;=&space;2$ [CBSE 2019] [4 Marks]
17. Prove that:
$\frac{tan^{3}\theta&space;}{1&space;+&space;tan^{2}\theta&space;}&space;+&space;\frac{cot^{3}\theta&space;}{1&space;+&space;cot^{2}\theta&space;}&space;=&space;sec&space;\theta&space;cosec&space;\theta&space;-&space;2&space;sin&space;\theta&space;cos&space;\theta$ [CBSE 2019] [4 Marks]