Is ((1+cos(2y)))/(sin^2(y))=2cot^2(y) ?

The answer to whether ((1+cos(2y)))/(sin^2(y))=2cot^2(y) is True

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prove ((1+cos(2y)))/(sin^2(y))=2cot^2(y)

prove

\frac{( 1 + cos ( 2 y ) )}{sin ^{2} ( y )} = 2 cot^{2} (y)

True

Solution steps

\frac{1 + cos ( 2 y )}{sin ^{2} ( y )} = 2 cot^{2} (y)

Manipulating left side

\frac{1 + cos ( 2 y )}{sin ^{2} ( y )}

Rewrite using trig identities

= \frac{2 cos ^{2} ( y )}{sin ^{2} ( y )}

Rewrite using trig identities

2 cot^{2} (y)

We showed that the two sides could take the same form

\Rightarrow True

4 cos^{2} (B) - 4 sin^{2} (B) = 4 - 8 sin^{2} (B)

\frac{( 1 - sin ^{2} ( x ) )}{cos ( x )} = cos (x)

sec^{2} (x) + 1 = \frac{1 + cos ^{2} ( x )}{cos ^{2} ( x )}

cos (4 A) = 8 cos^{4} (A) - 8 cos^{2} (A) + 1

cos (4 B) = 1 - 8 sin^{2} (B) + 8 sin^{4} (B)

Is ((1+cos(2y)))/(sin^2(y))=2cot^2(y) ?
The answer to whether ((1+cos(2y)))/(sin^2(y))=2cot^2(y) is True