Question #3260e

2 Answers
Nov 28, 2017

It cannot be verified. It is not an identity.

Explanation:

For x=pi/2 we get

LHS = 1 and RHS = 0

Nov 28, 2017

The left side should read (SinXCosX) + Cos^2X

Explanation:

Start with the Right Side:
RS = (CosX(1+CotX))/CscX
Now use the trig identities CotX = CosX/SinX and CscX= 1/SinX :
RS = (CosX(1 + CosX/SinX) )/(1/SinX)
Get a common denominator inside the bracket in the numerator, and multiply the entire numerator of the fraction by the reciprocal of the denominator:
RS = CosX(SinX/SinX + CosX/SinX)(SinX/1)

Add the fractions inside the bracket:
RS = CosX((SinX+ CosX)/SinX)(SinX/1)

The factor SinX in the numerator of the fraction on the right cancels with the denominator SinX leaving

RS=CosX(SinX+CosX)

Then distribute CosX into the brackets:
RS = CosXSinX + Cos^2X
This statement is what should be on the Left Side to make the identity.