Is ((1+cot^2(x)))/(sec^2(x))=cot^2(x) ?

The answer to whether ((1+cot^2(x)))/(sec^2(x))=cot^2(x) is True

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prove ((1+cot^2(x)))/(sec^2(x))=cot^2(x)

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Rewrite using trig identities

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

Rewrite using trig identities

cot^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

cot (s) + tan (s) = sec (s) csc (s)

cos (- \frac{π}{4}) = sin (\frac{π}{4})

sin (u) cos (u) = \frac{1}{2} sin (2 u)

(cot (x) - 1)^{2} = csc^{2} (x) - 2 cot (x)

cot (2 θ) = \frac{( cot ^{2} ( θ ) - 1 )}{2 cot ( θ )}

Is ((1+cot^2(x)))/(sec^2(x))=cot^2(x) ?
The answer to whether ((1+cot^2(x)))/(sec^2(x))=cot^2(x) is True