Is 1+(tan^2(θ))/(sec(θ)+1)=sec(θ) ?

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

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prove 1+(tan^2(θ))/(sec(θ)+1)=sec(θ)

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

= sec (θ)

We showed that the two sides could take the same form

\Rightarrow True

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

cot^{2} (θ) - cot^{2} (θ) = cos^{2} (θ) cot^{2} (θ)

tan (2 π - θ) = - tan (θ)

sin^{4} (θ) - cos^{4} (θ) = 1 - 2 cos^{2} (θ)

\frac{1 + tan ( x )}{1 - tan ( x )} + \frac{1 + cot ( x )}{1 - cot ( x )} = 0

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