Question

please let me know the answer​

Answer 1

Answer:

Given:

$\dfrac{1}{1+tan^2\theta} + \dfrac{1}{1+cot^2\theta} = ?$

Solution:

$\implies \dfrac{1}{1+tan^2 \theta} + \dfrac{1}{1+cot^2 \theta}$

$\implies \dfrac{1}{sec^2 \theta} + \dfrac{1}{cosec^2\theta}$

$\implies cos^2\theta + sin ^2 \theta$

$\boxed{\implies{\boxed{ = 1}}}$

Identities used:

1️⃣ $1 + tan^2 \theta = sec^2 \theta$

2️⃣ $1 + cot^2 \theta = cosec^2 \theta$

3️⃣ $cosec^2 \theta = \dfrac{1}{cos^2 \theta}$

4️⃣ $sec^2 \theta = \dfrac{1}{sin^2 \theta}$

5️⃣ $sin^2 \theta + \cos^2\theta = 1$

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