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FInd the smallest positive root of the \sqrt{\cos(1-x)}=\sqrt \sin x

Option: 1

\frac{\pi}{4}-\frac{1}{2}


Option: 2

\frac{\pi}{4}+\frac{1}{2}


Option: 3

\frac{\pi}{2}-\frac{1}{2}


Option: 4

None of these


Answers (1)

best_answer

Simultaneous Trigonometric Equations -

Simultaneous Trigonometric Equations

 

We can divide the problems related to Simultaneous Trigonometric Equations into two categories:

  1. If two equations satisfies simultaneously having only one unknown.

  2. If two equations satisfies simultaneously having two unknowns.

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\sqrt{\cos(1-x)}=\sqrt {\sin x}\\ \cos (1-x) \geq 0 \ \ and\ \sin x \geq 0\\ \cos(1-x)=\sin x\\ \sin (\frac{\pi}{2}-(1-x))=\sin x\\ \frac{\pi}{2}-1+x=n\pi + (-1)^n x \\ at\ n=1\\ 2x=\frac{\pi}{2}+1\\ x=\frac{\pi}{4}+\frac{1}{2}\\ \text{For this value of x } both\ satisfies\ \cos (1-x) \geq 0 \ \ and\ \sin x \geq 0\\

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manish painkra

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