Prove that: tanα / (1 +tan^2 α)^2 + cotα / (1+ cot^2 α)^2 = sinα. Cosα.

Answer:



Just for our easiness, I have solved and found the value of (1+ cot²α)²  first. I opened up the formula of (a+b)² = a² +2ab +b²

And then changed the cot into tan as
Cotx = 1/ tanx


Then I took the LHS and started solving the question .
I took the LCM and performed the basic Mathematics.
Then there is a step where I wrote
 cotα * tan⁴α = tan³α
It is because
Cotα = 1/ tanα
So
1/ tanα * tan⁴α = tan³α

Then I also used the Trigonometric identity of 1
Where sec² x - tan² x = 1

And the remaining processes, you can see in the figure above.
This is the way how you solve the given trigonometric identity of Trigonometry in mathematics.

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