sech-1(sinθ) is equal to
logtanθ2
logsinθ2
logcosθ2
logcotθ2
Explanation for the correct option:
Find the value of given expression:
As we know,
sech-1(x)=log[1+(1–x2)x]
Substituting x=sinθ,
sech-1(sinθ)=log1+(1–sin2θ)sinθ=log(1+cos2θ)sinθ=log(1+cosθ)sinθ=log1+cos2θ2–sin2θ22sinθ2cosθ2=logcos2θ2+cos2θ22sinθ2cosθ2=log2cos2θ22sinθ2cosθ2=log(cotθ2) ….[∵cosθ=cos2θ2-sin2θ2,sinθ=2sinθ2cosθ2,sin2θ+cos2θ=1]
Hence, Option ‘D’ is Correct.
If cos θ−tan θ=sec θ,then,θ is equal to