If sin C=\(\frac {15}{17}\) , find the value of sin A.

4

(a)

In a \(\triangle ABC,\angle B={ 90 }^{ 0 }\) .  If AB=2 cm and AC=3 cm, find the value of sin A,

4

(a)

If 17 cosA = 8, find 15 cosecA - 8 sec B.

4

(a)

Find the value of
(i) \(\sin { \theta } \cos { \theta } \)   for \(\theta ={ 30 }^{ 0 }\)
(ii) \(3\tan ^{ 2 }{ { 45 }^{ 0 } } +2\sin { { 45 }^{ 0 } } \cos { { 45 }^{ 0 } } \)

4

(a)

If \(\sin { \theta } -\cos { \theta } =0,(0\le \theta \le { 90 }^{ 0 })\) find the value of \(\theta \) .

4

(a)

Determine the value of x, such that
\(2{ cosec }^{ 2 }{ 30 }^{ 0 }+x\sin ^{ 2 }{ { 60 }^{ 0 } } -\frac { 3 }{ 4 } \tan ^{ 2 }{ { 30 }^{ 0 } } =10.\)

4

(a)

If A, B, C are the angles of a \(\triangle ABC,\) prove that \(\tan { \left( \frac { B+C }{ 2 } \right) } =\ cot { \frac { A }{ 2 } } .\)

4

(a)

Find the value of \(({ cosec }^{ 2 }\theta -1)\tan ^{ 2 }{ \theta } .\)

4

(a)

Prove that \(\sec ^{ 2 }{ \theta } -\frac { \sin ^{ 2 }{ \theta } -2\sin ^{ 4 }{ \theta } }{ 2\cos ^{ 4 }{ \theta } -\cos ^{ 2 }{ \theta } } =1\)

4

(a)

Given that 2 sin A cos A + (cos A + sin A)² - (2 cos A + sin A)² = p sin² A + q. Find the value of p and q.

4

(a)