The angles of a triangle are in A.P. and the greater angle is double the least angle. Find the angles of the triangle in radians.

5

(a)

Find the values of other five trigonometric functions cos x =\(-{1\over2},\) x lies in third quadrant.

5

(a)

Find the values of other five trigonometric functions cot x = \(3\over4\) ,x lies in third quadrant.

5

(a)

If sin \(\theta\) =\(-5\over 13\) and \(\theta\) lies in third quadrant, find the value of sec \(\theta\) + tan \(\theta\).

5

(a)

Prove the following:
\({sin \ x + sin \ 3x\over cos \ x + cos \ 3x}=\tan 2x\)

5

(a)

Find the general solution for each of the following equations:
sin x + sin 3x + sin 5x = 0

5

(a)

prove that:
\({({sin \ 7x}+ sin 5x) +(sin 9x + sin 3x)\over (cos 7x + cos 5x) + (cos 9x + cos 3x)}=\tan6x\)

5

(a)

Prove: \(sin\frac{B-C}{2}=\frac{b-c}{a}cos\frac{A}{2}.\)

5

(a)

Prove: \(\frac{cosA}{a}+\frac{cosB}{b}+\frac{cosC}{c}=\frac{a^2+b^2+c^2}{2abc}.\)

5

(a)