Mathematics, 03.01.2020 00:31 jfiicoh
Use trigonometric identities and algebraic methods, as necessary, to solve the following trigonometric equation. identify all possible solutions by including all answers in [0,2ï€) and indicating the remaining answers by using n to represent any integer. round your answer to four decimal places, if necessary. if there is no solution, indicate "no solution." cos2(5x)=sin2(5x)
Answers: 1
![[tex]\cos^2(5x)=\sin^2(5x)\qquad\text{substitute}\ t=5x\\\\\cos^2t=\sin^2t\qquad\text{use}\ \sin^2\theta+\cos^2\theta=1\to\sin^2\theta=1-\cos^2\theta\\\\\cos^2t=1-\cos^2t\qquad\text{add}\ \cos^2t\ \text{to both sides}\\\\2\cos^2t=1\qquad\text{divide both sides by 2}\\\\\cos^2t=\dfrac{1}{2}\Rightarrow \cos t=\pm\sqrt{\dfrac{1}{2}}\\\\\cos t=\pm\dfrac{\sqrt2}{2}\\\\\cos t=-\dfrac{\sqrt2}{2}\Rightarrow t=\pm\dfrac{3\pi}{4}+2n\pi\\\\\cos t=\dfrac{\sqrt2}{2}\Rightarrow t=\pm\dfrac{\pi}{4}+2n\pi](/tpl/images/0440/5104/3342f.png)
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