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## EXERCISE 3.3 1. Find values of: * sin $\frac{\pi}{3}$ * cos $\frac{\pi}{3}$ 2. Find sin 2x, cos 2x, tan 2x if secx = $\frac{13}{5}$, $-\frac{\pi}{2}$ < x < $\frac{\pi}{2}$ 3. Prove the following: * i) $\frac{1-cos 2\theta}{1+ cos2\theta}$ = tan2$\theta$ * ii) (sin2t - sin2x)sin(x+...

## EXERCISE 3.3 1. Find values of: * sin $\frac{\pi}{3}$ * cos $\frac{\pi}{3}$ 2. Find sin 2x, cos 2x, tan 2x if secx = $\frac{13}{5}$, $-\frac{\pi}{2}$ < x < $\frac{\pi}{2}$ 3. Prove the following: * i) $\frac{1-cos 2\theta}{1+ cos2\theta}$ = tan2$\theta$ * ii) (sin2t - sin2x)sin(x+t) + (cos2t - cos2x)cos(x+t) = 0 * iii) (cos2x - cos2y)2 + (sin2x - sin2y)2 = 4sin2($\frac{x+y}{2}$)sin2($\frac{x-y}{2}$) * iv) (cos2x - cos2y)2 + (sin2x - sin2y)2 = 4sin2($\frac{x+y}{2}$)sin2($\frac{x-y}{2}$) * v) tanx + cotx = 2 cosec 2x * vi) $\frac{cosx + sinx}{cosx-sinx}$ - $\frac{cosx - sinx}{cosx + sinx}$ = 2 tan 2x * vii) $\sqrt{2 + \sqrt{2 + \sqrt{2 + cosx}}}$ = 2 cos($\frac{x}{8}$) * viii) 16 sinx cosx cos2x cos4x cos8x = sin 16x * ix) $\frac{sin3x + cos3x}{sinx + cosx}$ = 2 cos2x