Is (sec^2(x)-6tan(x)+7)/(sec^2(x)-5)=(tan(x)-4)/(tan(x)+2) ?

The answer to whether (sec^2(x)-6tan(x)+7)/(sec^2(x)-5)=(tan(x)-4)/(tan(x)+2) is True

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prove (sec^2(x)-6tan(x)+7)/(sec^2(x)-5)=(tan(x)-4)/(tan(x)+2)

prove

\frac{sec ^{2} ( x ) - 6 tan ( x ) + 7}{sec ^{2} ( x ) - 5} = \frac{tan ( x ) - 4}{tan ( x ) + 2}

True

Solution steps

\frac{sec ^{2} ( x ) - 6 tan ( x ) + 7}{sec ^{2} ( x ) - 5} = \frac{tan ( x ) - 4}{tan ( x ) + 2}

Manipulating left side

\frac{sec ^{2} ( x ) - 6 tan ( x ) + 7}{sec ^{2} ( x ) - 5}

Rewrite using trig identities

= \frac{tan ( x ) - 4}{tan ( x ) + 2}

We showed that the two sides could take the same form

\Rightarrow True

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

cos (3 A) = 4 cos^{3} (A) - 3 cos (A)

sin (a) cot (a) = cos (a)

cos (3 θ) = cos^{3} (θ) - 3 sin^{2} (θ) cos (θ)

(sin (x) + cos (x))^{2} = 1 + sin^{2} (x)

Is (sec^2(x)-6tan(x)+7)/(sec^2(x)-5)=(tan(x)-4)/(tan(x)+2) ?
The answer to whether (sec^2(x)-6tan(x)+7)/(sec^2(x)-5)=(tan(x)-4)/(tan(x)+2) is True