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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

We showed that the two sides could take the same form

\Rightarrow True

sec (x) + tan (x) = (\frac{1}{sec ( x ) - tan ( x )})

(sec (a) - tan (a)) (sec (a) + tan (a)) = 1

sec (x - \frac{π}{2}) = csc (x)

cos (2 v) = \frac{1 - tan ^{2} ( v )}{1 + tan ^{2} ( v )}

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

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