Which of the following equations is an identity a SinX1cosx

Which of the following equations is an identity?

a. Sin(X)=1-cos(x)

b. Sin^2(x)-1=tan^2(x)

c. Cos(2x)=2cos(x)sin(x)

d. 2csc(2x)=sec(x)csc(x)

Solution

(d) 2csc(2x) = sec(x)csc(x)

=> 2/sin(2x) = 1/{sin(x)cos(x)}

=> sin(2x) = 2sin(x)cos(x)

which is an identity.