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How do you prove   $\frac{\tan{2A}}{1+\sec{2A}} = \tan{A}$
in Grade 12 Maths by Diamond (40.1k points) | 12 views

1 Answer

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RHS:

$\tan A=\dfrac{\sin A}{\cos A}$

multiply and divide by $2\cos A$

$\tan A=\dfrac{2\sin A\cos A}{2\cos^2 A}$

$\tan A=\dfrac{\sin 2A}{\cos^2 A+\cos^2 A}$

$\tan A=\dfrac{\sin 2A}{1−\sin^2 A+\cos^2 A}$

$\tan A=\dfrac{\sin 2A}{1+\cos^2 A}$

Divide numerator and denominator with $\cos 2A$

$\tan A = \dfrac{\tan 2A}{1+\sec 2A}$ proven.
by Silver Status (31.3k points)

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