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

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

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prove tan^2(A)+1=(sec(A))/(cos(A))

prove

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

True

Solution steps

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

Manipulating left side

tan^{2} (A) + 1

Express with sin, cos

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

Rewrite using trig identities

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

Manipulating right side

\frac{sec ( A )}{cos ( A )}

Express with sin, cos

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

We showed that the two sides could take the same form

\Rightarrow True

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

tan^{2} (x) - sin^{2} (x) = tan (x) sin (x)

sec (- x) = - sec (x)

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

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

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