Question

I. 1.
Prove that sin 50° - sin 70° + sin 10° =0.​

Answer 1

Answer:

GIVEN THAT sin 50 - sin 70 + sin 10

We take sin 50 and sin 10 first and the question as: sin 50+sin 10-sin 70

Since sin A+sin B= 2*sin{ (A+B)/2 }*cos {(A-B)/2}

so

sin 50+sin 10= 2sin (60/2)*cos (40/2)

= 2sin 30 cos 20

Sin 30=1/2

so 2 sin30cos20= 2*1/2*cos20

= cos 20

cos 20= cos(90–70)

=sin 70

Thus sin 70-sin 70=0.

Hence sin50-sin70+sin10=0

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Answer 2

Answer:

2sin( 50-70/2) cos(50+70/2) + sin 10

2sin(-10) cos60 + sin 10

2*1/2 sin (-10) + sin 10

-sin 10 + sin 10

=0

therefore

LHS = RHS

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