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Question Number 33413 by Rio Mike last updated on 15/Apr/18

$$$$$$thevalueof\theta ,intherange0°⩽\theta ⩽90°$$$$forwhichsin\theta =cos\theta is...?$$

Commented by Rasheed.Sindhi last updated on 16/Apr/18

$$\sin \theta =\cos (90-\theta )$$$$\theta =90-\theta$$$$2\theta =90$$$$\theta =45$$$$\sin 45=\cos 45$$$$$$

Commented by abdo imad last updated on 17/Apr/18

$$sin\theta =cos\theta \iff sin\theta =sin(\frac{\pi }{2}-\theta )\iff \theta =\frac{\pi }{2}-\theta +2k\pi or$$$$\theta =\pi -(\frac{\pi }{2}-\theta )+2k\pi (k\in Z)\iff 2\theta =\frac{\pi }{2}+2k\pi or\theta =\frac{\pi }{2}+\theta +2k\pi$$$$\iff \theta =\frac{\pi }{4}+k\pi butwehave0⩽\theta ⩽\frac{\pi }{2}\Rightarrow 0⩽\frac{\pi }{4}+k\pi ⩽\frac{\pi }{2}$$$$\Rightarrow 0⩽\frac{1}{4}+k⩽\frac{1}{2}\Rightarrow -\frac{1}{4}⩽k⩽\frac{1}{4}\Rightarrow k=0\Rightarrow \theta =\frac{\pi }{4}.$$

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