Question

Prove that:
cos^3(20)+sin^3(10)=3/4(cos20+sin10)

Answer 1

Answer:

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Step-by-step explanation:

we know,

4cos2x = 3cosx + cos3x

put here, x = = 20°

then, 4 cos 20° = 3cos20° + cos3 x 20°

3cos20° + cos60° =

cos 20° = (3cos20° + cos60°)/4 ......1

similarly,

4sinx = 3sinx - sin3x

put here, x = 10°

4sin 10° = 3sin 10° - sin30°

sin 10° = (3sin1O° - sin30°)/4 .........2

now,

LHS = cos 20° + sin 310° put equations (1) and (2)

= 1/4(3cos20° + cos60°) + 1/4 ( 3sin10° -

sin30°)

= 1/4( 3 cos 20° + cos60° + 3sin10° - sin30°)

we know,

cos60° = sin30° = 1/2

= 1/4 (3 cos 20° + 3sin10°)

= 3/4(cos20° + sin10°) = RHS

hence proved