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The second equation implies Multiply the equation by to obtain The first equation implies then Let Since the function is increasing where therefore As a conclusion,

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[Solved] Trigonometric equations

Trigonometry 1 & 2

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June 15, 2021 3:10 pm

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June 15, 2021 3:10 pm

Topic starter

Staff

(@armor)

Admin

Honorable Member

317 Posts
156 153 0

The second equation implies $\small 4y^3+sinycosy=-a.$

Multiply the equation by $\small -2$ to obtain $\small (-2y)^3+sin(-2y)=2a.$

The first equation implies $\small x^3+sinx=2a,$ then $\small f(x)=f(-2y).$

Let $\small f(t)=t^3+sint.$ Since the function $\small f(t)$ is increasing where $\small t\epsilon [-\frac{\Pi }{2},\frac{\Pi }{2}]\Rightarrow x=-2y,$

therefore $\small x+2y=0.$

As a conclusion, $\small cos(x+2y)=1.$

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