prove that \(\frac { sinA }{ 1+cosA } =\frac { 1-cosA }{ sinA } \) 

prove that \(\frac { sec\theta }{ sin\theta } -\frac { sin\theta }{ cos\theta } =cot\theta \)

From the top of a rock \(50\sqrt { 3 } \)m high, the angle of depression of a car on the ground is observed to be 30°. Find the distance of the car from the rock.

The horizontal distance between two buildings is 70 m. The angle of depression of the top of the first building when seen from the top of the second building is 45°. If the height of the second building is 120 m, find the height of the first building.

A player sitting on the top of a tower of height 20 m observes the angle of depression of a ball lying on the ground as 60°. Find the distance between the foot of the tower and the ball.(\(\sqrt { 3 } \) = 1.732)

The horizontal distance between two buildings is 140 m. The angle of depression of the top of the first building when seen from the top of the second building is 30° . If the height of the first building is 60 m, find the height of the second building.(\(\sqrt { 3 } \) = 1.732)

prove the following identitity tan⁴\(\theta \) + tan²\(\theta \) = sec⁴\(\theta \) - sec²\(\theta \) .

prove the following identity.
\(\frac { cos\theta }{ 1+sin\theta } \) = sec \(\theta \) - tan \(\theta \)

prove the following identities
\(\sqrt { \frac { 1+sin\theta }{ 1-sin\theta } } +\sqrt { \frac { 1+sin\theta }{ 1-sin\theta } } =2sec\theta \)

calculate \(\angle \)BAC inthe given triangles ( tan 69.4° = 2.6604 )