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Which trigonometric formula (or identity) should you use to help simplify and solve the equation \cos(2x) - \sin(x) = 1cos(2x)−sin(x)=1

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abidemiokin

The  trigonometric formula (or identity) should you use to help simplify and solve the equation is [tex]cos2x = 1-2sin^2x[/tex]

Trigonometry identity

Given the trigonometry identity

  • [tex] \cos(2x) - \sin(x) = 1[/tex]

According to trigonometry identity

  • [tex]cos(2x) = cos^2x-sin^2x\\ [/tex]

Also since [tex]cos^2x = 1-sin^2x[/tex], the expression becomes;

[tex]cos2x = (1-sin^2x)-sin^2x\\ cos2x = 1- 2sin^2x[/tex]

To simplify the function given, you will substitute [tex]cos2x = 1-2sin^2x[/tex] into the original equation to have:

[tex] \cos(2x) - \sin(x) = 1\\ (1-2sin^2x)-sinx=1\\ [/tex]

Hence the  trigonometric formula (or identity) should you use to help simplify and solve the equation is [tex]cos2x = 1-2sin^2x[/tex]

Learn more on trig identity here: https://brainly.com/question/24496175

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