Is (1+sec(θ))(1-sec(θ))=-tan^2(θ) ?

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

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prove (1+sec(θ))(1-sec(θ))=-tan^2(θ)

prove

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

True

Solution steps

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

Manipulating left side

(1 + sec (θ)) (1 - sec (θ))

Expand

(1 + sec (θ)) (1 - sec (θ)) : 1 - sec^{2} (θ)

= 1 - sec^{2} (θ)

Use the Pythagorean identity:

sec^{2} (θ) = tan^{2} (θ) + 1

sec^{2} (θ) - 1 = tan^{2} (θ)

= - tan^{2} (θ)

We showed that the two sides could take the same form

\Rightarrow True

cos (x) = \frac{cot ( x )}{csc ( x )}

sin (\frac{3 π}{2} - x) = - cos (x)

sin (x) sec (x) = \frac{1}{cot ( x )}

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

1 - cos^{2} (θ) = sin^{2} (θ)

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