Question

If phi+theta=60°
So, Prove That Sin(120°-theta)= Cos(30°-phi)

Answer 1

Here is the ans
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Answer 2

Given:

Ф + θ = 60°

To prove that: $\sin (120-\theta)$ = $\cos(30-\phi)$.

L.H.S. = $\sin (120-\theta)$

∵ Ф + θ = 60°

⇒ θ = 60°  - Ф

= $\sin (120-(60-\phi))$

= $\sin (120-60+\phi)$

= $\sin (60+\phi)$

Using the trigonometric identity:

$\cos A$ = $\sin (90-A)$

= $\cos (90-60-\phi)$

= $\cos(30-\phi)$

= R.H.S., proved.

Thus, $\sin (120-\theta)$ = $\cos(30-\phi)$, proved.