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#### Trigonometry Five Marks Questions

10th Standard EM

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Maths

Time : 01:00:00 Hrs
Total Marks : 50
10 x 5 = 50
1. If sin (A - B) = $\frac12$,  cos (A + B) = $\frac12$, 0o < A + ≤  90°, A > B, find A and B.

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

3. If sin 3A = cos (A - 26°), where 3A is an acute angle, find the value at A.

4. If ATB=90o then prove that
$\sqrt { \frac { tanA\quad tanB+tanA\quad cotB }{ sinA\quad secB } } -\frac { { Sin }^{ 2 }A }{ { Cos }^{ 2 }A } =tanA$

5. P.T (1+tan∝tan∝tanβ)2 +(tan∝-tanβ)2 =sec2 ∝sec2β.

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

7. $P.T\left( \frac { 1+{ tan }^{ 2 }A }{ 1+{ cot }^{ 2 }A } \right) ={ \left( \frac { 1-tan\quad A }{ 1-cot\quad A } \right) }^{ 2 }={ tan }^{ 2 }A$

8. If tanθ+sinθ=P; tanθ-sinθ=q P.T P2-q2=4$\sqrt{pq}$

9. The angle of elevation of a tower at a point is 45o, After going 20 meters towards the foot of the tower the angle of elevation of the tower becomes 60o calculate the height of the tower.

10. 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