Prove that: 
(3 - 4 sin^2 α) /(1- 3tan^2 α) = (3 -tan^2 α) (4cos^2 α -3)

Answer:


For solving such type of question, we need to understand the concept that we will already have two common terms in LHS and the RHS.


let's find them here. Tan^2 α common so let us operate on it.

Taking LHS
We will not touch the first term until we solve the second term
As you can see in the image. We solved the second term whose numerator will be equal to the second term of RHS.

But since the denominator is not needed in that place we shift it in first term and it will be correct because they are in multiple form.

Then we perform the operations on the first term as well and prove that the LHS is equal to the RHS.

The Trigonometric identity used:

Tan x = sinx /cosx
1/ Cox = secx


This is how you prove that the LHS is equal to the RHS in Trigonometric questions in Trigonometry.
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