Using trigonometric identities, the solution to the equation[tex]cos(\frac{\pi }{2} -x) = \frac{\sqrt{3} }{2}[/tex] for all possible values of x on the interval [0, 2π].
What are trigonometric identities?
Trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined.
[tex]cos(\frac{\pi }{2} - x) = \frac{\sqrt{3} }{2} \\\\cos(x) cos(\frac{\pi }{2}) + sin(x) sin(\frac{\pi }{2}) = \frac{\sqrt{3} }{2} \\\\cos(x) (0)+sin(x)(1) = \frac{\sqrt{3} }{2} \\\\sin(x) = \frac{\sqrt{3} }{2}\\\\x = \frac{\pi }{3} , \frac{2\pi }{3}[/tex]
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