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Question Number 146404 by iloveisrael last updated on 13/Jul/21

$$\mathrm{trigonometry}$$

Commented by iloveisrael last updated on 13/Jul/21

Answered by gsk2684 last updated on 13/Jul/21

$$f\left(x\right)=\frac{1-\cos {}^{2}x+{\cos }^{4}x}{1-\sin {}^{2}x+\sin {}^{4}x}$$$$=\frac{1-\cos {}^{2}x(1-{\cos }^{2}x)}{1-\sin {}^{2}x(1-{\sin }^{2}x)}$$$$=\frac{1-\cos {}^{2}x\sin {}^{2}x}{1-\sin {}^{2}x\cos {}^{2}x}=1$$$$f\left(x\right)=1\mathrm{\forall }x$$

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