Sin^2(x)-cos^2(x)= sin^2(x)+cos^2(x) Find exact solutions between 0 and 2π How should I solve this?

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Sin^2(x)-cos^2(x)= sin^2(x)+cos^2(x) Find exact solutions between 0 and 2π How should I solve this?

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Answer 1 · 2017-05-26T01:10:57

$\frac{π}{2}; \frac{3 π}{2}$ $pi/2 ; (3pi)/2$

Explanation:

${sin}^{2} x - {cos}^{2} x = {sin}^{2} x + {cos}^{2} x = 1$ $sin^2 x - cos^2 x = sin^2 x +cos^2 x = 1$
Replace ${cos}^{2} x$ $cos^2 x$ by $(1 - {sin}^{2} x)$ $(1 - sin^2 x)$ :
${sin}^{2} x - 1 + {sin}^{2} x = 1$ $sin^2 x - 1 + sin^2 x = 1$
$2 {sin}^{2} x = 2$ $2sin^2 x =2$ --> ${sin}^{2} x = 1$ $sin^2 x = 1$ -->
$sin x = \pm 1$ $sin x = +- 1$
Unit circle gives -->
$x = \frac{π}{2} and x = \frac{3 π}{2}$ $x = pi/2 and x = (3pi)/2$

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Sin^2(x)-cos^2(x)= sin^2(x)+cos^2(x) Find exact solutions between 0 and 2π How should I solve this?

1 Answer

Explanation:

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