The value of \(si{ n }^{ 2 }\theta +\frac { 1 }{ 1+ta{ n }^{ 2 }\theta } \) is equal to

If sin \(\theta \) + cos\(\theta \) = a and sec \(\theta \) + cosec \(\theta \) = b, then the value of b(a² - 1) is equal to 

(1 + tan \(\theta \) + sec\(\theta \)) (1 + cot\(\theta \) - cosec\(\theta \)) is equal to 

The electric pole subtends an angle of 30° at a point on the same level as its foot. At a second point ‘b’ metres above the first, the depression of the foot of the pole is 60°. The height of the pole (in metres) is equal to

A tower is 60 m height. Its shadow is x metres shorter when the sun’s altitude is 45° than when it has been 30°, then x is equal to

Two persons are standing ‘x’ metres apart from each other and the height of the first person is double that of the other. If from the middle point of the line joining their feet an observer finds the angular elevations of their tops to be complementary, then the height of the shorter person (in metres) is

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

prove that\(\left( \frac { co{ s }^{ 3 }A-si{ n }^{ 3 }A }{ cosA-sinA } \right) -\left( \frac { co{ s }^{ 3 }A+si{ n }^{ 3 }A }{ cosA+sinA } \right) =2sinAcosA\)

If \(\frac { co{ s }^{ 2 }\theta }{ sin\theta } \) = p and \(\frac { sin^{ 2 }\theta }{ cos\theta } \) = q, then prove that p²q²(p² + q² + 3) = 1

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.

As shown in the figure, Two trees are standing on the flat ground. the angel of elevation of the top of both the trees from a point x on the ground is 40° .if the horizontal distance between x and the smaller tree is 8m and the distance of the top of the trees is 20m, calculate, the distance between the point x and the top of the smaller tree.

prove the following identities.
\(\frac { sinA-sinB }{ cosA+cosB } +\frac { cosA-cosB }{ sinA+sinB } =0\)