Is tan^2(θ)+1= 1/(cos^2(θ)) ?

The answer to whether tan^2(θ)+1= 1/(cos^2(θ)) is True

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prove tan^2(θ)+1= 1/(cos^2(θ))

prove

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

True

Solution steps

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

Manipulating left side

tan^{2} (θ) + 1

Express with sin, cos

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

Rewrite using trig identities

= \frac{1}{cos ^{2} ( θ )}

We showed that the two sides could take the same form

\Rightarrow True

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

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

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

sin^{2} (x) cos (x) sec (x) = 1 - cos^{2} (x)

tan^{2} (x) cos^{2} (x) = 1 - cos^{2} (x)

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