Question

prove that Sin 34°+cos 64°- cos 4°=0

Answer 1

Sin34° + Cos64° - Cos4°
= Sin34° + Cos(34 + 30)° - Cos(34 - 30)°
= Sin34° + (-2Sin34°Sin30°)
= Sin34° - 2 × Sin34° × 1/2
= Sin34° - Sin34°
= 0 (Proved)

Answer 2

$\sin 34+\cos 64-\cos 4=0$, proved.

Step-by-step explanation:

Prove that, $\sin 34+\cos 64-\cos 4=0$

L.H.S. $=\sin 34+\cos 64-\cos 4$

$=\sin 34+\cos (34+30)-\cos (34-30)$

$=\sin 34+\cos 34\cos 30-\sin 34\sin 30-(\cos 34\cos 30+\sin 34\sin 30)$

Using trigonometric identity,

$\cos (A+B)=\cos A\cos B-\sin A\sin B$ and

$\cos (A-B)=\cos A\cos B+\sin A\sin B$

$=\sin 34+\cos 34\cos 30-\sin 34\sin 30-\cos 34\cos 30-\sin 34\sin 30$

$=\sin 34-\sin 34\sin 30-\sin 34\sin 30$

$=\sin 34-2\sin 34\sin 30$

$=\sin 34-2\sin 34(\dfrac{1}{2})$

$=\sin 34-\sin 34$

= 0

= R.H.S., proved

Hence, $\sin 34+\cos 64-\cos 4=0$, proved.