Question

one upon sec square theta minus cos square theta + 1 upon cos squared theta minus sin square theta + sin square theta is equal to 1 minus sin square theta cos square theta upon 2 + sin square theta cos square theta prove it

Answer 1

Solution :-

Since Cos (A+B) = cosAcosB – sinAsinB,

Putting

A= B, Cos2A = cos^A - sin^A,

Therefore,

Sin^ (theta) - cos^ (θ) = -cos(2× θ).

Now

cos(θ) is -1 to 1,

Therefore,

Range of sin^(θ) - cos^(θ) is -1 to 1.

So its value can never be 2.

They both get cancelled.

===============

@GauravSaxena01