[(sinθ tanθ + cosθ)2 - 1] is equal to:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 I.e. tan2θ.
(sinθ tanθ + cosθ)2 - 1
= [sinθ(sinθ/cosθ) + cosθ]2 - 1
= [sin2θ/cosθ + cosθ]2 - 1
= [(sin2θ + cos2θ)/cosθ]2 - 1
= (1/cosθ)2 - 1
= sec2θ - 1
= tan2θ