Question

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

Answer 1

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Answer 2

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