Question

Find the value of 4cos^3 20°-3cos20°​

Answer 1

we know

4cos³x=3cosx+cos3x

put here,x=20°

then,4cos³=3cos20°+cos³*20°

=3cos20°+cos60°

cos³20°=(3cos20°+cos60°)/4

similarly

4sin³x=35inx-in3x

put here,x=10°

4sin³10°=35in10°-sin30°

sin³10°=(35in10°-sin30)/4

how

LHS=cos³20°+sin³10°

put equations (1)and(2)1/4(3cos20°+cos60°+3sin10°=sin30°)

we know

cos69°=sin30°=1/2

1/4(3cos20°+3sin10°)

=3/4(cos20°+sin10°)=RHS

hence proved