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  • If <img alt="6\cos 2\Theta +2\cos ^{2}\Theta /2+2\sin ^{2}\Theta =0,-\pi <\Theta <\pi ," src="https://learn.careers360.com/latex-image/?6%5Ccos%202%5CTheta%20&plus;2%5Ccos%20%5E%7B2%7D%5C

If 6\cos 2\Theta +2\cos ^{2}\Theta /2+2\sin ^{2}\Theta =0,-\pi <\Theta <\pi , then \Theta=

 

Option: 1

\pi/3
 


Option: 2

\pi/3,\cos ^{-1}(3/5)


Option: 3

\cos ^{-1}(3/5)

 


Option: 4

\pi/3,\pi-\cos ^{-1}(3/5)


Answers (1)

best_answer

 

Double Angle Formula -

Double angle formula

- wherein

These are formulae for double angles.

 

 

12\cos ^{2}\Theta -6+1+\cos \Theta +2-2\cos ^{2}\Theta =0

Or 10\cos ^{2}\Theta +\cos \Theta -3=0

Or (5\cos \Theta +3)(2\cos \Theta-1)=0

\Rightarrow \cos \Theta =-\frac{3}{5},\frac{1}{2}

\Rightarrow \Theta =\frac{\pi}{3},\pi-\cos ^{-1}\left ( \frac{3}{5} \right ),-\frac{\pi}{3}

Posted by

Riya

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