Find the value of tan² 10° - cot² 80°.

Find the value of sin² 41° + sin² 49°.

An observer 1.2 metere tall is 28.2 m away from the tower.The angle of elevation of the top of the tower from his eye is 60°.What is the height of the tower?

In given figure, if AB = 4 m and AC = 8 rn, then find the angle of elevation of A as observed from C.

If the altitude of the Sun is 60°, what is the height of a tower which casts a shadow of length 30m?

Eliminate \(\theta\) from the following equation. \(x=k+a\cos { \theta } ,y=h+b\sin { \theta } \)

If \(\sqrt { 3 } \cot ^{ 2 }{ \theta } -4\cot { \theta } +\sqrt { 3 } =0,\) find the value of the \(\tan ^{ 2 }{ \theta } +\cot ^{ 2 }{ \theta } .\)

Evaluate : \(\frac { \cos { { 45 }^{ ° } } }{ \sec { { 30 }^{ ° } } } +\frac { 1 }{ \sec { { 60 }^{ ° } } } \)

If \(\sin { A } =\frac { \sqrt { 3 } }{ 2 } \), find the value of \(2\cot ^{ 2 }{ A } -1\)

A player sitting on the top ofa tower of height 20m 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.

What happens to value of \(\tan { \theta } \) when \(\theta\) increases from 0⁰ to 90⁰ ?

Evaluate \(\cos { { 53 }^{ 0 } } -\sin { { 37 }^{ 0 } } \)

Prove that cot A + tan A = sec A cosec A.

If \(\sin { A } =\frac { 1 }{ \sqrt { 5 } } \quad and\quad \sin { B } =\frac { 1 }{ \sqrt { 10 } } ,\) find the values of cos A and cos B. Hence using the formula cos (A + B) = cos A cos B - sin A sin B, show that A + B + 45⁰ .

Prove that \(sinAcosA-\frac { sinAcos(90°-A)cosA }{ sec(90°-A) } -\frac { cosAsin(90°-A)sinA }{ cosec(90°-A) } .\)

In a \(\triangle ABC,\) right angled at A, having AB=5 cm, and BC=12 cm, find sin B, cos C and tan B.

If \(\triangle ABC\) is right angles at C, find the value of cos (A + B).

Prove that \(\sqrt { \frac { \sin { A } +1 }{ 1-\sin { A } } } +\sqrt { \frac { 1-\sin { A } }{ \sin { A } +1 } } =2\sec { A } .\)

Express sin 67⁰ +cos 75⁰ in terms of trigonometric ratios of angles between 0⁰ and 45⁰ .