Question

help me to find the value​

Answer 1

Step-by-step explanation:

answer as shown above...

Answer 2

Answer:

3/10

Step-by-step explanation:

Given:

tanθ = 1/√2

We know that,

1 + cot²θ = cosec²θ

⇒ cosec²θ = cot²θ - 1

Therefore, the given expression can be written as,

$\frac{cosec^2\theta - sec^2\theta}{cosec^2\theta + cot^2\theta}$

$\Rightarrow \frac{cosec^2\theta - sec^2\theta}{1 + cot^2\theta + cot^2\theta}$

$\Rightarrow \frac{cosec^2\theta - sec^2\theta}{1+2cot^2\theta}$

$\Rightarrow \frac{1 + cot^2\theta - (1 + tan^2\theta)}{1 + 2cot^2\theta}$

$\Rightarrow \frac{cot^2\theta-tan^2\theta}{1 + 2cot^2\theta}$

$tan\theta = \frac{1}{\sqrt{2}} \ \Rightarrow cot \theta = {\sqrt{2}}$

$\Rightarrow \frac{(\sqrt{2})^2 - (\frac{1}{\sqrt{2}})^2}{1 + 2 * (\sqrt{2})^2}$

$\Rightarrow \frac{2 - \frac{1}{2}}{1 + 2 * 2}$

$\rightarrow \boxed {\frac{3}{10}}$

Hope it helps!