Question

sin(150+x)+sin(150-x)equelcosx

Answer 1

Answer :

Sin ( 150 + x ) + Sin ( 150 - x ) = Cos x

LHS : -

Sin ( 150 + x ) + Sin ( 150 - x )

We know that $Sin x + Sin y = 2 * Sin (\frac{x+y}{2}) * Cos (\frac{x-y}{2} )$

So,

$Sin ( 150 + x ) + Sin ( 150 - x ) = 2 * Sin [\frac{150+x)+(150-x)}{2} ] * Cos [\frac{150+x)-(150-x)}{2} ] = 2 * Sin 150 * Cos x = 2 * Sin ( \pi -30 ) * Cos x = 2* Sin 30 * Cos x = Cos x * 2 * (\frac{1}{2}) = Cos x = RHS$