If tanθ2=t, then 1-t21+t2 is equal to
cos(θ)
sin(θ)
sec(θ)
cos(2θ)
Explanation for correct option
Trigonometry identity:
Given: 1-t21+t2
=1-tan2θ21+tan2θ2[∵tanθ2=t]=1-sin2θ2cos2θ21+sin2θ2cos2θ2[∵tan(θ)=sin(θ)cos(θ)]=cos2θ2-sin2θ2cos2θ2cos2θ2+sin2θ2cos2θ2=cos2θ2-sin2θ2cos2θ2+sin2θ2[∵cos2x-sin2x=cos(2x),cos2x+sin2x=1]=cos(θ)
Hence, option A is correct.