Prove that:
(1 - sin^4 A) / cos^4 A = 1 + 2 tan^2 A

Answer:


We need to remember the little thing which we used to follow Everytime in Trigonometry. The thing is:

a^2 - b^2 = (a +b) (a -b)

We do the same here and expand the term
1- sin^4 A

Then we use the Trigonometric identity:
1- sin^2 A = cos^2 A

Then we cancel the equal terms from numerator and denominator. I.e. cos^2 A

Since we have to get 2tan^2 A in the RHS, we need two sin^2 A in the numerator so, we expand 1 using the Trigonometric identity:
1 = sin^2 A + cos^2 A

And then we do simple division and match the terms to RHS.

Identity: tan x = sinx / cosx

So, this is the way to solve the Trigonometric identity of Trigonometry in mathematics.

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