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

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

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

prove

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

True

Solution steps

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

Manipulating left side

tan^{2} (x) + 1

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

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

cot (θ) + \frac{sin ( θ )}{1 + cos ( θ )} = csc (θ)

\frac{sin ( \frac{π}{2} + x )}{sin ( π - x )} = cot (x)

cos (x) \cdot csc (x) = cot (x)

sin (4 x) = 4 sin (x) cos (x) cos (2 x)

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