If sinA=\(\frac {12}{13}\) , what is the value of cos A?

4

(a)

If \(\sqrt { 3 } \sin { \theta } =\cos { \theta } \), find the value of \(\frac { \tan { \theta } (1+\cot { \theta } ) }{ \sin { \theta } +\cos { \theta } } .\)

4

(a)

Find the value of \((\sin { { 30 }^{ 0 } } +\cos { { 30 }^{ 0 } } )-(\sin { { 60 }^{ 0 } } +\cos { { 60 }^{ 0 } } ).\)

4

(a)

Evaluate \({ \left( \frac { \sin { { 25 }^{ 0 } } }{ \cos { { 65 }^{ 0 } } } \right) }^{ 2 }+{ \left( \frac { \tan { { 65 }^{ 0 } } }{ \cot { { 25 }^{ 0 } } } \right) }^{ 2 }-2\cos ^{ 2 }{ { 45 }^{ 0 } } .\)

4

(a)

Prove that \(\frac { \sec ^{ 2 }{ \theta } -\sin ^{ 2 }{ \theta } }{ \tan ^{ 2 }{ \theta } } =1+\cot ^{ 2 }{ \theta } -\cos ^{ 2 }{ \theta } \)

4

(a)

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

4

(a)

Show that \(\tan { { 48 }^{ 0 } } \tan { { 23 }^{ 0 } } \tan { { 42 }^{ 0 } } \tan { { 67 }^{ 0 } } =1.\)

4

(a)

Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
\(\sqrt { \frac { 1+\sin { A } }{ 1-\sin { A } } } =\sec { A } +\tan { A } \)

4

(a)

If tan A  = a tan B and sin A = b sin B, prove that \(\cos ^{ 2 }{ A } =\frac { { b }^{ 2 }-1 }{ { a }^{ 2 }-1 } \)

4

(a)

In the following figure, \(\triangle PQR\)  is right angled at Q, PQ=5 cm, PR=6cm. Determine \(\angle QPR and \angle PRQ.\)

4

(a)

In the following figure, find tan P - cot R.

4

(a)

Given that \(\left( A+B \right) =\frac { \tan { A } +\tan { B } }{ 1-\tan { A } \tan { B } } \), find the values of tan 75° and tan 90° by taking suitable values of A and B.

4

(a)

If \(\sec { \theta } +\tan { \theta } =p,\) show that \(\sec { \theta } -\tan { \theta } =\frac { 1 }{ p } \). Hence, find the values of \(\cos { \theta } \) and \(\sin { \theta } \).

4

(a)

The angle of elevation of a cloud from a point 120 m above a lake is 30° and the angle of depression of its reflection in the lake is 60°. Find the height of the cloud.

4

(a)

If \(cosec\theta +\cot { \theta } =p\), then prove that \(\cos { \theta } =\frac { { p }^{ 2 }-1 }{ { p }^{ 2 }+1 } \)

4

(a)