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

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

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

prove

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

True

Solution steps

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

Manipulating left side

sec^{2} (x) + 1

Express with sin, cos

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

We showed that the two sides could take the same form

\Rightarrow True

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

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

tan (θ) sin (θ) cos (θ) = sin^{2} (θ)

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

sin (\frac{π}{2} - u) = cos (u)

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