If sin (A - B) = \(\frac12\),  cos (A + B) = \(\frac12\), 0^o < A + ≤  90°, A > B, find A and B.

Express the ratios cos A, tan A and sec A in terms of sin A.

Evaluate \(\frac { tan{ 65 }^{ o } }{ tan{ 25 }^{ o } } \)

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

Express cot 85° + cos 75° in terms of trigonometric ratios of angles between 0° and 45°.

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.

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

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

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

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

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

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

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

Prove the trigonometric identity
\(\frac{\sin \theta}{1-\cos \theta}=\operatorname{cosec} \theta+\cot \theta\)

Prove the trigonometric identity
\(\frac{\tan \theta+\sin \theta}{\tan \theta-\sin \theta}=\frac{\sec \theta+1}{\sec \theta-1}\)