Prove that: tan^2 A + cot^2 A = sec^2 A.cosec^2 A - 2 

Answer:


Here, to solve the question, we used the Trigonometric identity of tan A and cotA
Which is

Tan A = Sin A / Cos A

And

Cot A = Cos A / Sin A
After that we took the LCM and then opened up the algebraic formula.

Algebraic formulas used:
a^2 + b^2 = (a + b)^2 - 2 ab OR (a - b)^2 + 2 ab

We need to analyze which formula should be used here.
Let's see the RHS, we have (- 2)

This means we need to use the formula of:

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

Then we expand the formula into it's factors and then use the Trigonometric identity:

Sin^2 x + cos^2 x = 1

And solved the question finally by changin
 1/cos A = secA
And
1/ sinA = cosecA

So, you can prove this Trigonometric identity of Trigonometry using this process.

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