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

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

p ro v e 1 + cos (x) \cdot sin (x) = sin (x)

p ro v e (sin (x)) \frac{1}{sin ( x )} = 1

p ro v e cos^{2} (2 x) = \frac{( 1 + cos ( 4 x ) )}{2}

p ro v e \frac{1 + sin ( x )}{cos ( x ) tan ( x ) - 1} = - 1

p ro v e \frac{sin ( x ) sec ( x )}{tan ( x )} = 1

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