If sin2Θ = cos3Θ, then the value of (cot2Θ - cot6Θ) is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. -1.
We have given in the question,
sin2Θ = cos3Θ
Square on both sides
sin4Θ = cos6Θ
So, the value of (cot2Θ - cot6Θ)
= (cot2Θ - cos6Θ/sin6Θ)
= (cot2Θ - cos6Θ/sin6Θ)
= (cot2Θ - sin4Θ/sin6Θ)
= (cot2Θ - 1/sin2Θ)
= (cot2Θ - cosec2Θ)
= -1