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  • If sqroot 3 tan θ = 1, then find the value of sin power 2 θ – cos power 2θ.

If \sqrt{3}  tan θ = 1, then find the value of sin2θ – cos2θ.

Answers (1)

   Given :

\sqrt{3}\tan\theta=1  
\tan \theta = \frac{1}{\sqrt{3}}
\theta = 30^{\circ}       \left ( \because \tan30^{\circ}= \frac{1}{\sqrt{3}} \right )
\sin ^{2}\theta -\cos ^{2}\theta = \sin ^{2}30^{\circ}-\cos ^{2}30^{\circ}
(Because θ = 300)
= \left ( \frac{1}{2} \right )^{2}-\left ( \frac{\sqrt{3}}{2} \right )^{2}         \begin{bmatrix} \because \sin 30^{\circ}= \frac{1}{2} & \\ \cos 30^{\circ}= \frac{\sqrt{3}}{2}& \end{bmatrix}
= \frac{1}{4}-\frac{3}{4}

Taking L.C.M.
= \frac{1-3}{4}= \frac{-2}{4}
\sin ^{2}\theta -\cos ^{2}\theta = \frac{-1}{2}

 

 

Posted by

infoexpert27

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