Is (1+tan^2(θ))/(sec(θ))=sec(θ) ?

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

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prove (1+tan^2(θ))/(sec(θ))=sec(θ)

prove

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

True

Solution steps

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

Manipulating left side

\frac{1 + tan ^{2} ( θ )}{sec ( θ )}

Rewrite using trig identities

= sec (θ)

We showed that the two sides could take the same form

\Rightarrow True

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)

\frac{cot ( - θ )}{csc ( θ )} = - cos (θ)

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