Question

Explain the approach you would take to verify that the following equation is an identity and why youwould choose that approach. Do not actually verify that the equation is an identity. (4 points)= csc(2x) + 1(sin(x) + cos(x))²sin(2x)

Answer 1

Given the expression

$\frac{(sin(x)+cos(x))^2}{sin(2x)}=csc(2x)+1$

Solving the perfect square

$\frac{sin^2(x)+2sin(x)cos(x)+cos^2(x)}{s\imaginaryI n(2x)}=csc(2x)+1$$\frac{1+2sin(x)cos(x)}{s\imaginaryI n(2x)}=csc(2x)+1$

Sin(2x) equals to

$sin(2x)=2sin(x)cos(x)$

then

$\frac{1+2s\imaginaryI n(x)cos(x)}{s\imaginaryI n(2x)}=csc(2x)+1$$\frac{1+sin(2x)}{sin(2x)}=csc(2x)+1$$\frac{1}{sin(2x)}+\frac{sin(2x)}{sin(2x)}=csc(2x)+1$$\frac{1}{sin(2x)}+1=csc(2x)+1$$csc(2x)+1=csc(2x)+1$