Convert the following into radians.
520^o

3

(a)

Express the following in radians.
40^o 20'

3

(a)

If cosec \(A=\frac { x }{ y } \), then find the value of cot A.

3

(a)

Prove the following identities.
\(\frac { tan\theta +sec\theta -1 }{ tan\theta -sec\theta +1 } =\frac { 1+sin\theta }{ cos\theta } \)

3

(a)

Prove that \(\frac { { cos15 }^{ 0 }+{ sin15 }^{ 0 } }{ { cos15 }^{ 0 }-{ sin15 }^{ 0 } } =\sqrt { 3 } \)

3

(a)

Find the value of sin 10⁰ + sin 50⁰ - sin 70⁰

3

(a)

Find the general solution of the equation 2cos²x+3sinx=0

3

(a)

Prove that \(\frac { sinx }{ cos3x } +\frac { sin3x }{ cos9x } +\frac { sin9x }{ cos27x } =\frac { 1 }{ 2 } \left( tan27x-tanx \right) .\)

3

(a)

If \(tan\alpha =\frac { 1 }{ 7 } ,sin\beta =\frac { 1 }{ \sqrt { 10 } } \). Prove that \(\alpha +2\beta =\frac { \pi }{ 4 } \) , where \(0<\alpha <\frac { \pi }{ 2 } \quad and\quad 0<\beta <\frac { \pi }{ 2 } .\)

3

(a)

Find the values of the trigonometric function \(tan({-17\pi\over6})\)

3

(a)

The perimeter of a certain sector of a circle is equal to the length of the arc of a semi-circle having the same radius. Express the angle of the sector in degrees, minutes and seconds.

3

(a)

If sin\(\theta\) = n sin (\(\theta\) + 2\(\alpha\).), prove that tan (\(\theta\)+\(\alpha\))\(=({1+n\over 1-n})tan \alpha\)

3

(a)

Find the following values: cos 18°

3

(a)

Find the following values: cos 36°

3

(a)

Find the following values: sin 36°

3

(a)