Is cot^4(x)=(cos^4(x))/(sin^4(x)) ?

The answer to whether cot^4(x)=(cos^4(x))/(sin^4(x)) is True

Popular >

prove cot^4(x)=(cos^4(x))/(sin^4(x))

prove

cot^{4} (x) = \frac{cos ^{4} ( x )}{sin ^{4} ( x )}

True

Solution steps

cot^{4} (x) = \frac{cos ^{4} ( x )}{sin ^{4} ( x )}

Manipulating left side

cot^{4} (x)

Express with sin, cos

cot^{4} (x)

Use the basic trigonometric identity:

cot (x) = \frac{cos ( x )}{sin ( x )}

= (\frac{cos ( x )}{sin ( x )})^{4}

Simplify

(\frac{cos ( x )}{sin ( x )})^{4} : \frac{cos ^{4} ( x )}{sin ^{4} ( x )}

(\frac{cos ( x )}{sin ( x )})^{4}

Apply exponent rule:

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

= \frac{cos ^{4} ( x )}{sin ^{4} ( x )}

= \frac{cos ^{4} ( x )}{sin ^{4} ( x )}

= \frac{cos ^{4} ( x )}{sin ^{4} ( x )}

We showed that the two sides could take the same form

\Rightarrow True

\frac{1}{1 - sin ( x )} + \frac{1}{1 + sin ( x )} = 2 sec (x)

cos^{4} (b) - sin^{4} (b) = cos (2 b)

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

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

(6 cos^{2} (x) - 6 sin^{2} (x)) = 6 - 12 sin^{2} (x)

Is cot^4(x)=(cos^4(x))/(sin^4(x)) ?
The answer to whether cot^4(x)=(cos^4(x))/(sin^4(x)) is True