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The general solution of the equation 2 cot \frac{\theta }{2}=(1+ cot \theta )^{2} is :

Option: 1

n\pi+(-1)^{n} \frac{\pi}{4},n\epsilon I


Option: 2

n\pi+(-1)^{n} \frac{\pi}{3},n\epsilon I


Option: 3

n\pi+(-1)^{n} \frac{\pi}{6},n\epsilon I


Option: 4

none


Answers (1)

best_answer

As we have learnt in

 

Trigonometric Ratios of Submultiples of an Angle -

Trigonometric ratios of submultiples of an angle 1

- wherein

This shows the formulae for half angles and their doubles.

 

 

General Solution of Trigonometric Ratios -

\sin \Theta = \sin \alpha

\Theta = n\pi + \left ( -1 \right )^{n}\alpha , n\epsilon I

- wherein

\alpha is the given angle

 

 

\frac{2.2\cos\theta /2.\cos\theta/2}{2\sin\theta /2.\cos\theta/2}=\left ( 1+\cot\theta \right )^{2}

or \frac{2(1+\cos\theta )}{\sin\theta }=cosec^{2}\theta+2\cot\theta

or 2+2cos\theta=cosec\theta+2cos\theta

or \sin\theta=1/2 \Rightarrow \theta =n\pi+(-1)^{n}\frac{\pi}{6}

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