The value of [tan2θ - sin2θ]/[2 + tan2θ + cot2θ] is :
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e sin6θ
[tan2θ - sin2θ]/[2 + tan2θ + cot2θ]
= [sin2θ (1/cos2θ - 1)]/[2 + tan2θ + cot2θ]
= [sin2θ(sec2θ - 1)]/[2 + tan2θ + cot2θ]
= (sin2θ.tan2θ)/(tanθ + cotθ)2
= sin2θ.tan2θ/(1/sin2θ.cos2θ)
= sin6θ