Is (tan^2(x))/(sin^2(x))=1+tan^2(x) ?

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

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prove (tan^2(x))/(sin^2(x))=1+tan^2(x)

prove

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

True

Solution steps

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

Manipulating left side

\frac{tan ^{2} ( x )}{sin ^{2} ( x )}

Express with sin, cos

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

Manipulating right side

1 + tan^{2} (x)

Express with sin, cos

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

Rewrite using trig identities

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

We showed that the two sides could take the same form

\Rightarrow True

sin^{2} (x) + cos^{2} (x) = cos (x) sec (x)

sec (y) + tan (y) = \frac{cos ( y )}{1 - sin ( y )}

(csc (x) + cot (x)) (sec (x) - 1) = tan (x)

cos (x - \frac{π}{2}) = cos (x) tan (x)

csc (- θ) = - csc (θ)

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