If sin2 θ = cos3 θ, then the value of (cot2 θ - cot6 θ) is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. -1
Given that
If sin2 θ = cos3 θ
sin2 θ/cos2 θ = cos θ
so, tan2 θ = cos θ
and cot2 θ = sec θ
Hence, the value of (cot2 θ - cot6 θ) = sec θ - sec3 θ = sec θ (1 - sec2 θ)
= cot2 θ ( - tan2 θ) = cot2 θ × -1/cot2 θ = -1