Prove that: cot^2 Θ - cos^2Θ = cot^2 Θ cos^2 Θ

Answer:


In the given question, it might feel that the identity is impossible to solve initially. But relax, think widely!

We know, cot^2 Θ = cos^2 Θ / sin^2 Θ

And when we take LCM after expanding
 cot^2 Θ
We get something common in the numerator!
When we take the common term and write the remaining terms we get (1- sin^2 Θ) which is equal to cos^2 Θ [ an important Trigonometric identity] . Then it's easy to solve the question. See the picture above to visualize the answer now!

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