If cosec ∅ = √2, find the value of 1+sin²∅+cos²∅/1+sec²∅-tan²∅.

Given:  

∴

=

∴

METHOD 1: Using Trigonometric values.

We have given that,

So,

We need to find:

So,

METHOD 2: Using Trigonometric Identities

We need to find:

But, we know that,

And,

So,

Therefore, by both methods the answer is 1.

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Prove that:

\cos( \frac{3\pi}{2} + \theta) \cos(2\pi + \theta) [ \cot( \frac{3\pi}{2} - \theta) + \cot(2\pi + \theta) ] = 1...

no solution

step-by-step explanation:

there is not enough information in the problem to solve.