Is tan^4(x)=tan^2(x)sec^2(x)-tan^2(x) ?

The answer to whether tan^4(x)=tan^2(x)sec^2(x)-tan^2(x) is True

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prove tan^4(x)=tan^2(x)sec^2(x)-tan^2(x)

prove

tan^{4} (x) = tan^{2} (x) sec^{2} (x) - tan^{2} (x)

True

Solution steps

tan^{4} (x) = tan^{2} (x) sec^{2} (x) - tan^{2} (x)

Manipulating right side

tan^{2} (x) sec^{2} (x) - tan^{2} (x)

Rewrite using trig identities

= tan^{4} (x)

We showed that the two sides could take the same form

\Rightarrow True

(tan (θ) + cot (θ)) cos (θ) = csc (θ)

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

\frac{sec ( x ) + csc ( x )}{1 + tan ( x )} = csc (x)

1 + tan^{2} (- θ) = sec^{2} (θ)

\frac{tan ( x ) + tan ( y )}{cot ( x ) + cot ( y )} = tan (x) tan (y)

Is tan^4(x)=tan^2(x)sec^2(x)-tan^2(x) ?
The answer to whether tan^4(x)=tan^2(x)sec^2(x)-tan^2(x) is True