Question

prove sin( 150+x)+sin (150-x)=cosx

Answer 1

Heya !!


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Here's your answer !!!

solve for x:

sin(250-x)+sin(x+150) = cos(x)
subtract cos (x) from both sides:-
cos(x) + sin(150-x)+sin(x+150) = 0

simplify trigonometric function :-
(-1 + sin(150)2) cos(x) = 0
divide both side by -1+2 sin(150):
cos(x) = 0

take the inverse cosine of both side:
answer: |
| x = pi/2+pi*n for n element Z

in the first quadrant, x = pi/2 radians,
= 90 degree.
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hope it helps you☻☻