2tan-1(cosx)=tan-1(cosec2x),thenx=
π2
π
π6
π3
Find the value of given equation:
2tan-1(cosx)=tan-1(cosec2x)
⇒ 2cosx1-cos2x=1sin2x ∵2tan-1x=(2x1-x2)
⇒ 2cosxsin2x=1sin2x ∵1-cos2x=sin2x
⇒ 2cosx=1
⇒ cosx=12
⇒ x=π3 ∵-1≤cosx≤1
Hence, Option ‘D’ is Correct.
x^2+1/x^2=47 then x^2-1/x^2=?