Just clarify your basics

Geometry Level 1

Which of the given options is equal to tan ⁡ 2 θ \tan2\theta ?

tan ⁡ 2 ( θ ) 2 tan ⁡ 2 ( 2 θ ) \dfrac{\tan^2{(\theta)}}{2{\tan}^2(2\theta)} tan ⁡ ( θ ) 1 + tan ⁡ ( 2 θ ) \dfrac{\tan(\theta)}{1 + \tan(2\theta)} tan ⁡ ( θ ) \tan(\theta) 2 tan ⁡ ( θ ) 1 − tan ⁡ 2 ( θ ) \dfrac{2\tan(\theta)}{1 - {\tan}^2(\theta)}

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Ashish Menon by Ashish Menon , 20, India

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1 solution

Ashish Menon
May 3, 2016

tan ⁡ ( 2 θ ) = tan ⁡ ( θ + θ ) = tan ⁡ ( θ ) + tan ⁡ ( θ ) 1 − tan ⁡ ( θ ) × tan ⁡ ( θ ) = 2 tan ⁡ ( θ ) 1 − tan ⁡ 2 ( θ ) \begin{aligned} \tan(2\theta) & = \tan(\theta + \theta)\\ & = \dfrac{\tan(\theta) + \tan(\theta)}{1 - \tan(\theta) × \tan(\theta)}\\ & = \boxed{\dfrac{2\tan(\theta)}{1 - {\tan}^2(\theta)}} \end{aligned}

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Hi bro, how r u

Rishabh Sood - 5 years, 1 month ago

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Nice problem by the way

Rishabh Sood - 5 years, 1 month ago

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I am fine thanks.

Ashish Menon - 5 years, 1 month ago

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