11+tan2θ+11+cot2θ=

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Question

$\frac{1}{1 + t a n^{2} θ} + \frac{1}{1 + c o t^{2} θ} =$

Options:

A . -1

B . 0

C . 1

D . 2

Answer: Option C
:
C

We know that, $1 + t a n^{2} θ = s e c^{2} θ and 1 + c o t^{2} θ = c o s e c^{2} θ$
$\frac{1}{1 + t a n^{2} θ} + \frac{1}{1 + c o t^{2} θ} = \frac{1}{s e c^{2} θ} + \frac{1}{c o s e c^{2} θ}$
$= c o s^{2} θ + s i n^{2} θ$

$= 1$

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