Question

Evaluate : 1+tan2A / 1+cot2A

Answer 1

Formula used:

Tan A = sinA/cosA

Cot A= cosA / sinA

Sin²A+ cos²A= 1
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Answer:
1+tan²A/1+cot²A = tan²A
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Hope this will help you...

Answer 2

The correct answer is = $\frac{2tan A}{1-tan^{2}A }$.

Given: $\frac{1+tan2A}{1+cot2A}$

To Find: The value of this expression.

Solution:

$\frac{1+tan2A}{1+cot2A}$

= $\frac{1+tan2A}{1+\frac{1}{tan2A} }$

= $\frac{(1+tan2A)tan2A}{1+tan2A}$

= tan 2A

tan 2A = $\frac{sin 2A}{cos2A}$    (Sin 2A = 2SinACosA and Cos 2A = $cos^{2}x- sin^{2}x$ )

= $\frac{2SinACosA}{cos^{2}x- sin^{2}x}$

= $\frac{2tanACos^{2}A }{Cos^{2}A(1-tan^{2} A) }$

= $\frac{2tan A}{1-tan^{2}A }$

Hence, the expression after solving gives = $\frac{2tan A}{1-tan^{2}A }$.

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