Is tan^4(x)=(1-sec^2(x))^2 ?

The answer to whether tan^4(x)=(1-sec^2(x))^2 is True

Popular >

prove tan^4(x)=(1-sec^2(x))^2

prove

tan^{4} (x) = (1 - sec^{2} (x))^{2}

True

Solution steps

tan^{4} (x) = (1 - sec^{2} (x))^{2}

Manipulating right side

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

Rewrite using trig identities

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

Use the Pythagorean identity:

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

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

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

Simplify

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

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

Apply exponent rule:

(- a)^{n} = a^{n},

n

is even

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

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

Apply exponent rule:

(a^{b})^{c} = a^{b c}

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

Multiply the numbers:

2 \cdot 2 = 4

= tan^{4} (x)

= tan^{4} (x)

= tan^{4} (x)

We showed that the two sides could take the same form

\Rightarrow True

- 2 sin (x) = - sin (2 x)

\frac{1}{1 - \frac{1}{( 1 - \frac{1}{( 1 - c o s h ^{2} ( x ) )} )}} = cosh^{2} (x)

(\frac{sec ( θ )}{cos ( θ )}) - (\frac{tan ( θ )}{cot ( θ )}) = 1

sin (π) = sin (3 π)

cos^{2} (x) sin^{2} (x) + cos^{4} (x) = cos^{2} (x)

Is tan^4(x)=(1-sec^2(x))^2 ?
The answer to whether tan^4(x)=(1-sec^2(x))^2 is True