Is (tan^2(θ)+1)/(sec(θ))=sec(θ) ?

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

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prove (tan^2(θ)+1)/(sec(θ))=sec(θ)

prove

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

True

Solution steps

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

Manipulating left side

\frac{tan ^{2} ( θ ) + 1}{sec ( θ )}

Rewrite using trig identities

\frac{tan ^{2} ( θ ) + 1}{sec ( θ )}

Use the Pythagorean identity:

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

= \frac{sec ^{2} ( θ )}{sec ( θ )}

Cancel the common factor:

sec (θ)

= sec (θ)

= sec (θ)

We showed that the two sides could take the same form

\Rightarrow True

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

3 cos (2 x + \frac{π}{2}) - 2 = 6 cos^{2} (x + \frac{π}{4})

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

cot^{4} (x) = \frac{cos ^{4} ( x )}{sin ^{4} ( x )}

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

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