Question

Verify the identity. cotangent x equals StartFraction 1 plus cosine 2 x Over sine 2 x EndFractioncot x= 1+cos2x sin2x Use the appropriate​ double-angle formulas to rewrite the numerator and denominator of the expression on the right. For the denominatordenominator​, use the​ double-angle formula that will produce only one term in the denominatordenominator when it is simplified.

Answer 1

Answer with Step-by-step explanation:

We are given that

RHS

$\frac{1+Cos2x}{Sin2x}$

We have to verify the identity.

We know that

$1+Cos2x=2Cos^2 x$

$Sin2x=2SinxCos x$

Using the formula

$\frac{2Cos^2x}{2SinxCosx}$

$\frac{Cosx}{Sinx}$

$Cot x$

By using the formula

$Cotx=\frac{Cosx}{Sinx}$

LHS=RHS

Hence, verified