Is tan^6(x)=tan^4(x)sec^2(x)-tan^4(x) ?

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

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prove tan^6(x)=tan^4(x)sec^2(x)-tan^4(x)

prove

tan^{6} (x) = tan^{4} (x) sec^{2} (x) - tan^{4} (x)

True

Solution steps

tan^{6} (x) = tan^{4} (x) sec^{2} (x) - tan^{4} (x)

Manipulating right side

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

Rewrite using trig identities

= tan^{6} (x)

We showed that the two sides could take the same form

\Rightarrow True

\frac{1 + cos ( 2 x )}{sin ( 2 x )} = \frac{1}{tan ( x )}

cos (2 x) = cos (x + x)

\frac{csc ( a )}{cot ( a ) + tan ( a )} = cos (a)

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

sec (x) sin (x) = tan (x)

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