Is tan(x)(sec^2(x)-1)=tan^3(x) ?

The answer to whether tan(x)(sec^2(x)-1)=tan^3(x) is True

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prove tan(x)(sec^2(x)-1)=tan^3(x)

prove

tan (x) (sec^{2} (x) - 1) = tan^{3} (x)

True

Solution steps

tan (x) (sec^{2} (x) - 1) = tan^{3} (x)

Manipulating left side

tan (x) (sec^{2} (x) - 1)

Rewrite using trig identities

tan (x) (sec^{2} (x) - 1)

Use the Pythagorean identity:

sec^{2} (x) = tan^{2} (x) + 1

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

= tan (x) tan^{2} (x)

Simplify

tan (x) tan^{2} (x) : tan^{3} (x)

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

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

tan (x) tan^{2} (x) = tan^{1 + 2} (x)

= tan^{1 + 2} (x)

Add the numbers:

1 + 2 = 3

= tan^{3} (x)

= tan^{3} (x)

= tan^{3} (x)

We showed that the two sides could take the same form

\Rightarrow True

sin (x) = - 1

sec (b) + tan (b) = \frac{cos ( b )}{1 - sin ( x )}

2 sinh (ln (x)) + \frac{1 ^{2}}{2} - \frac{4}{3} = 2

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

\frac{1}{tan ( x )} - tan (x) = 2 cot (2 x)

Is tan(x)(sec^2(x)-1)=tan^3(x) ?
The answer to whether tan(x)(sec^2(x)-1)=tan^3(x) is True