Question

Tan(π/4+A/2) -Tan (A/2-π/4)= 2 secA

Answer 1

Answer:

The given equation is:

tan({\frac{\pi}{4}+x)+tan({\frac{\pi}{4}-x)=2sec2x

Taking the LHS of the above equation, we get

tan({\frac{\pi}{4}+x)+tan({\frac{\pi}{4}-x)=\frac{1+tanx}{1-tanx}+\frac{1-tanx}{1+tanx}

=\frac{(1+tanx)^{2}+(1-tanx)^2}{1-tan^2x}

=\frac{2(1+tan^2x)}{(1-tan^2x)}

=\frac{2(cos^2x+sin^2x)}{cos^2x-sin^2x}

=\frac{2}{cos2x}

=2sec2xl

=RHS

Hence proved

Step-by-step explanation:

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