Question

If theta = 30 , verify that tan 2theta = 2 tan theta/ 1+ tan^2 theta​

Answer 1

Secondary SchoolMath 5+3 pts

If theta =30°,verify that cos2theta=1-tan^2theta/1+tan^2theta

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Given:\theta=30^{\circ}

To verify: \cos2\theta=\dfrac{1-\tan^2\theta}{1+\tan^2\theta}

Calculation:

First we take left side and put\theta=30^{\circ}

\Rightarrow \cos2(30^{\circ})

\Rightarrow \cos60^{\circ}

\Rightarrow \dfrac{1}{2}

Now we take right side and put \theta=30^{\circ}

\Rightarrow \dfrac{1-\tan^2\theta}{1+\tan^2\theta}

\Rightarrow \dfrac{1-\tan^230^{\circ}}{1+\tan^230^{\circ}}

\Rightarrow \dfrac{1-\frac{1}{3}}{1+\frac{1}{3}}

\Rightarrow \dfrac{3-1}{3+1}

\Rightarrow \dfrac{1}{2}

LHS=RHS=\dfrac{1}{2}

Hence verified

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