Question

solve this question......​

Answer 1

Answer:

3/10

Step-by-step explanation:

Given,

tan∅ = (1/√2)

Then,

cot ∅ = √2

We know that,

cosec²∅ - cot²∅ = 1     ----- (1)

cosec²∅ = 1 + cot²∅    ---- (2)

Now,

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

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

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

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

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

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

Hope it helps!