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  • If 2sin2θ – cos2θ = 2, then find the value of θ.

If 2sin2θ – cos2θ = 2, then find the value of θ.

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  2sin2θ – cos2θ = 2
2\left ( 1-\cos ^{2}\theta \right )-\cos ^{2}\theta = 2           \left ( \because \sin ^{2}\theta +\cos ^{2}\theta= 1 \right )
2-2\cos ^{2}\theta-\cos ^{2}\theta= 2
2-3\cos ^{2}\theta-2= 0
-3\cos ^{2}\theta= 0
\cos ^{2}\theta= 0
\cos \theta= 0
\theta= 90^{\circ}           \left ( \because \cos 90^{\circ}= 0 \right )

 Hence value of \theta is 90°

 

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infoexpert27

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