Is (1-sin^2(x))*csc^2(x)=cot^2(x) ?

The answer to whether (1-sin^2(x))*csc^2(x)=cot^2(x) is True

Popular >

prove (1-sin^2(x))*csc^2(x)=cot^2(x)

prove

(1 - sin^{2} (x)) \cdot csc^{2} (x) = cot^{2} (x)

True

Solution steps

(1 - sin^{2} (x)) csc^{2} (x) = cot^{2} (x)

Manipulating right side

cot^{2} (x)

Express with sin, cos

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

Rewrite using trig identities

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

Use the basic trigonometric identity:

\frac{1}{sin ( x )} = csc (x)

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

We showed that the two sides could take the same form

\Rightarrow True

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

cot^{2} (θ) - cos^{2} (θ) = cot^{2} (θ) cos^{2} (θ)

\frac{sin ^{2} ( - x )}{tan ^{2} ( x )} = cos^{2} (x)

\frac{1 + cos ( θ )}{cos ( θ )} = sec (θ) + 1

\frac{1 + sec ( θ )}{tan ( θ ) + sin ( θ )} = csc (θ)

Is (1-sin^2(x))*csc^2(x)=cot^2(x) ?
The answer to whether (1-sin^2(x))*csc^2(x)=cot^2(x) is True