- (a) Use the identity
$$\cos ( A + B ) \equiv \cos A \cos B - \sin A \sin B$$
to prove that
$$\cos x \equiv 1 - 2 \sin ^ { 2 } \frac { x } { 2 }$$
(b) Prove that, for \(\sin x \neq 0\),
$$\frac { 1 - \cos x } { \sin x } \equiv \tan \frac { x } { 2 }$$
(c) Find the values of \(x\) in the interval \(0 \leq x \leq 360 ^ { \circ }\) for which
$$\frac { 1 - \cos x } { \sin x } = 2 \sec ^ { 2 } \frac { x } { 2 } - 5$$
giving your answers to 1 decimal place where appropriate.