If \(\sec ^{ 2 }{ \theta } =x+\frac { 1 }{ 4x } ,\) find the value of \(\sec { \theta } +\tan { \theta } .\)

2

(a)

Prove that \(\sqrt { \sec ^{ 2 }{ \theta } +{ cosec }^{ 2 }\theta } =\tan { \theta } +\cot { \theta } .\)

2

(a)

Eliminate  \(\theta\) from the following equation. \(x=a\sec { \theta } ,y=b\tan { \theta } \)

2

(a)

Using the formula, \(\cos { A } =\sqrt { \frac { 1+\cos { 2A } }{ 2 } } ,\) find the value of \(\cos { { 15 }^{ 0 } } \)

2

(a)

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

2

(a)

In the given figure, \(\triangle ABC,\) is the right angles at B. \(\triangle BSC\) is right angles at S and BC = 7.5 cm, RS = 5 cm, RB = 6 cm \(\angle BSR=x^0\) and \(\angle SAB=y^0.\)  Find

(i) tan x⁰
(ii) sin y
(ii) cos y⁰

2

(a)

Evaluate : \(\frac { \sin { { 90 }^{ ° } } }{ \cos { { 45 }^{ ° } } } +\frac { 1 }{ cosec{ 30 }^{ ° } } \)

2

(a)

If \(\sqrt { 2 } \sin { \theta } =1\), find the value of \(\sec ^{ 2 }{ \theta } -cosec^{ 2 }\theta \)

2

(a)

If 4 cos \(\theta\)  = 11 sin \(\theta\), find the value of \(\frac { 11\cos { \theta } -7\sin { \theta } }{ 11\cos { \theta } +7\sin { \theta } } \)

2

(a)

Prove that : \(-1+\frac { \sin { A } \sin { \left( { 90 }^{ ° }-A \right) } }{ \cot { \left( { 90 }^{ ° }-A \right) } } =-\sin ^{ 2 }{ A } \)

2

(a)

Prove that : \(\sqrt { \frac { 1-\cos { A } }{ 1+\cos { A } } } =cosecA-\cot { A } \)

2

(a)

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

2

(a)

From the top of light house, 40 m above the later, the angle of depression of a small boat is 60°. Find how far the boat is from the base of the light house.

2

(a)

From a point P on the ground the angle of elevation of the top of a 10 m tall building is 30°. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from P is 45°. Fin~ the length of the flagstaff and distance of building form point P.

2

(a)

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.

2

(a)