Evaluate tan-11+x2+1–x21+x2-1–x2
π4+12cos-1x2
π4+cos-1x2
π4+12cos-1x
π4-12cos-1x2
Explanation for correct option
Simplifying the given expression:
tan-11+x2+1–x21+x2-1–x2=tan-11+cos2α+1-cos2α1+cos2α-1-cos2α[Letx2=cos2α]
We know that:
cos2θ=2cos2θ-1⇒1+cos2θ=2cos2θ∴1+cos2α=2cos2α=2cosα------(1)
Also,
cos2θ=1-2sin2θ⇒1-cos2θ=2sin2θ∴1-cos2α=2sin2α=2sinα-----(2)
So, we get:
tan-12cosα+2sinα2cosα-2sinα=tan-12cosα2cosα+2sinα2cosα2cosα2cosα-2sinα2cosα=tan-11+tanα1-tanα=tan-1tanπ4+tanα1-tanπ4tanα[∵tanπ4=1]=tan-1tanπ4+α=π4+α=π4+12cos-1x2
Hence, the correct answer is option (A).
Evaluate the following:
513÷119