#### Trigonometry Model Question Paper

10th Standard EM

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Maths

Time : 01:00:00 Hrs
Total Marks : 50
4 x 1 = 4
1. If sinθ-cosθ=0, then the value of (sin4θ+cos4θ) is

(a)

1

(b)

$\frac{3}{4}$

(c)

$\frac{1}{2}$

(d)

$\frac{1}{4}$

2. The value of sin2θ +$\frac { 1 }{ 1+{ tan }^{ 2 }\theta }$ of

(a)

sin2θ

(b)

cos2θ

(c)

secθ

(d)

1

3. (cosec2θ-cot2θ) (1-cos2θ) is equal to

(a)

cosec θ

(b)

cos2θ

(c)

sec2θ

(d)

sin2θ

4. 9 sec2A -9tam2A=

(a)

1

(b)

9

(c)

8

(d)

0

5. 5 x 2 = 10
6. $1+\frac { { cot }^{ 2 }\alpha }{ 1+cosex\alpha } =cosec\alpha$

7. tan θ+tan(90o-θ)=secθ sec(90o-θ)

8. Simplify (1+tan2θ)(1-sinθ)(1+sinθ)

9. An observer 1.5 metres tall is 20.5 metres away from a tower 22 metres high. Determine the angle of elevation of the top of the tower from eye of the observer.

10. Show that tan4θ+tan2θ=sec4θ-sec2θ.

11. 4 x 5 = 20
12. If sin (A - B) = $\frac12$,  cos (A + B) = $\frac12$, 0o < A + ≤  90°, A > B, find A and B.

13. Express the ratios cos A, tan A and see A in terms-of sin A.

14. If 15tan2 θ+4 sec2 θ=23 then find the value of (secθ+cosecθ)2 -sin2 θ

15. The shadow of a tower, when the angle of elevation of the sum is 45o is found to be 10 metres, longer than when it is 60o. find the height of the tower

16. 2 x 8 = 16
17. Express cot 85° + cos 75° in terms of trigonometric ratios of angles between 0° and 45°.

18. From a point on a bridge across a river, the angles of depression of the banks on opposite sides at the river are 30° and 45°, respectively. If the bridge is at a height at 3 m from the banks, find the width at the river.