Question

Question #3260e

Answer 1

It cannot be verified. It is not an identity.

Explanation:

For `x=pi/2` we get

LHS = 1 and RHS = 0

Answer 2

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.