Is 4/(cos^2(x))-5=4tan^2(x)-1 ?

The answer to whether 4/(cos^2(x))-5=4tan^2(x)-1 is True

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prove 4/(cos^2(x))-5=4tan^2(x)-1

prove

\frac{4}{cos ^{2} ( x )} - 5 = 4 tan^{2} (x) - 1

True

Solution steps

\frac{4}{cos ^{2} ( x )} - 5 = 4 tan^{2} (x) - 1

Manipulating right side

4 tan^{2} (x) - 1

Express with sin, cos

= \frac{- cos ^{2} ( x ) + 4 sin ^{2} ( x )}{cos ^{2} ( x )}

Rewrite using trig identities

= \frac{- 5 cos ^{2} ( x ) + 4}{cos ^{2} ( x )}

Expand

\frac{4 - 5 cos ^{2} ( x )}{cos ^{2} ( x )} : \frac{4}{cos ^{2} ( x )} - 5

= - 5 + \frac{4}{cos ^{2} ( x )}

= \frac{4}{cos ^{2} ( x )} - 5

We showed that the two sides could take the same form

\Rightarrow True

(sec (x) + tan (x)) (1 - sec (x)) = cos (x)

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

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

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

\frac{1}{csc ( x )} + 1 = sin (x) + 1

Is 4/(cos^2(x))-5=4tan^2(x)-1 ?
The answer to whether 4/(cos^2(x))-5=4tan^2(x)-1 is True