Question

Prove that cos(60°-30°) =cos60°cos30°+sin60°sin30°

Answer 1

Answer:

it can be solve using the formula:-cos(A-B)=cosAcosB-sinAsinB

Answer 2

$\cos(60-30) =\cos 60\cos30+\sin60\sin30$, proved.

Step-by-step explanation:

Prove that $\cos(60-30) =\cos 60\cos30+\sin60\sin30$.

L.H.S. =$\cos(60-30)$

= $\cos 30$

= $\dfrac{\sqrt{3}}{2}$  [Since, $\cos 30$ = $\dfrac{\sqrt{3}}{2}$]

R.H.S. = $\cos 60\cos30+\sin60\sin30$

= $\cos (60-30)$

Using the trigonometric identity,

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

= $\cos 30$

= $\dfrac{\sqrt{3}}{2}$  [Since, $\cos 30$ = $\dfrac{\sqrt{3}}{2}$]

∵ L.H.S. = R.H.S. = $\dfrac{\sqrt{3}}{2}$, proved.

Thus, $\cos(60-30) =\cos 60\cos30+\sin60\sin30$, proved.