Question

Sin18°.cos39°+ +sin6°.cos15°=sin24°.cos33°

Answer 1

Answer:

Explanation:

=sin18cos39+sin6cos15

=Cos39sin18+cos15sin6

=1/2(sin57-sin21)+1/2(sin21-sin9)

=1/2(sin57-sin9)

=1/2(2(cos33)(sin24))

=sin24Cos33

Answer 2

Complete Question:

Prove that: sin18°.cos39°+ sin6°.cos15° = sin24°.cos33°

Complete Answer:

Given:

The equation sin18°.cos39°+ sin6°.cos15° = sin24°.cos33°

To Prove:

That the given equation is correct.

Calculation:

- Take LHS of the equation and evaluate:

LHS = sin18°.cos39°+ sin6°.cos15°

       = 1/2{sin (18 + 39) + sin (18 - 39)} + 1/2{sin(6+15) + sin(6-15)}

       = 1/2 [{sin 57 + sin (-21)} + { sin 21 + sin (-9)}]

       = 1/2[{sin 57 - sin 21} + { sin 21 - sin 9}]

       = 1/2(sin 57 - sin 9)

       = 1/2[2 cos {(57+9)/2}. sin {(57-9)/2}]

       = cos (66/2).sin 48/2

       = cos 33°.sin24°

      = RHS

Hence, proved.