Question

express the following as sum or difference of trigonometric ratios
2 cos 78° sin 42 °​

Answer 1

We know that,

$\sf{2\ \cos x\ \sin y=\sin (x+y)-\sin (x-y)}$

Then,

$\sf{2\cos 78^{\circ}\sin 42^{\circ}=\sin (78^{\circ}+42^{\circ})-\sin (78^{\circ}-42^{\circ})}\\\\\\\underline {\underline {\sf{2\cos 78^{\circ}\sin 42^{\circ}=\sin 120^{\circ}-\sin 36^{\circ}}}}$

Answer 2

Answer:

2cosAsinB

sin(A+B)-sin(A-B)

sin(78°+42°)-sin(78°-42°)

sin120°-sin36°

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