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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

= 1 + cos^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

sin (2 θ) = 2 cot (θ) sin^{2} (θ)

tan (θ) + 1 = sec (θ)

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

cos (θ) - cos^{3} (θ) = sin^{2} (θ) cos (θ)

2 sin (θ) cos (θ) = tan (2 θ) cos (2 θ)

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