Prove that tan²\(\theta \)-sin² \(\theta \) = tan² \(\theta \) sin² \(\theta \)

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

prove that 1+\(\frac { co{ t }^{ 2 }\theta }{ 1+cosec\theta } \) = cosec\(\theta \) 

prove that sec\(\theta \) - cos\(\theta \) = tan \(\theta \) sin\(\theta \) 

prove that \(\sqrt { \frac { 1+cos\theta }{ 1-cos\theta } } \) = cosec \(\theta \) + cot\(\theta \)

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

prove the following identity.
cot \(\theta \) + tan \(\theta \) = sec \(\theta \) cosec\(\theta \)

prove the following identities.\(\frac { 1-ta{ n }^{ 2 }\theta }{ co{ t }^{ 2 }\theta -1 } =ta{ n }^{ 2 }\theta \)

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

calculate \(\angle \)BAC in the given triangles (tan 38.7° = 0.8011 )

A tower stands vertically on the ground. from a point on the ground, which is 48m away from the foot of the tower, the angel of elevation of the top of  the tower is 30°.find the height of the tower.

Find the angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of a tower of height \(10\sqrt { 3 } m\)

A road is flanked on either side by continuous rows of houses of height \( 4\sqrt { 3 } \)m with no space in between them. A pedestrian is standing on the median of the road facing a row house. The angle of elevation from the pedestrian to the top of the house is 30°. Find the width of the road.

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.