Is prove-(-1+sin^2(θ))/(sin^2(θ))=cot^2(θ) ?

The answer to whether prove-(-1+sin^2(θ))/(sin^2(θ))=cot^2(θ) is True

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

prove-(-1+sin^2(θ))/(sin^2(θ))=cot^2(θ)

prove

- \frac{- 1 + sin ^{2} ( θ )}{sin ^{2} ( θ )} = cot^{2} (θ)

True

Solution steps

- \frac{- 1 + sin ^{2} ( θ )}{sin ^{2} ( θ )} = cot^{2} (θ)

Manipulating right side

cot^{2} (θ)

Express with sin, cos

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

Rewrite using trig identities

= \frac{- sin ^{2} ( θ ) + 1}{1 - cos ^{2} ( θ )}

Factor

\frac{1 - sin ^{2} ( θ )}{1 - cos ^{2} ( θ )} : \frac{- ( sin ( θ ) + 1 ) ( sin ( θ ) - 1 )}{- ( cos ( θ ) + 1 ) ( cos ( θ ) - 1 )}

= \frac{- ( - 1 + sin ( θ ) ) ( 1 + sin ( θ ) )}{- ( - 1 + cos ( θ ) ) ( 1 + cos ( θ ) )}

Expand

\frac{- ( - 1 + sin ( θ ) ) ( 1 + sin ( θ ) )}{- ( - 1 + cos ( θ ) ) ( 1 + cos ( θ ) )} : \frac{sin ^{2} ( θ ) - 1}{cos ^{2} ( θ ) - 1}

= \frac{- 1 + sin ^{2} ( θ )}{- 1 + cos ^{2} ( θ )}

Rewrite using trig identities

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

We showed that the two sides could take the same form

\Rightarrow True

cos (2 A + A) = - 3 cos (A) + 4 cos^{3} (A)

tan (x) cos^{2} (x) csc^{2} (x) = cot (x)

(sin^{2} (x) + cos^{2} (x))^{3} = 1^{3}

cos (- x) \cdot cot (x) + sin (x) = csc (x)

\frac{0}{sin ( θ )} = \frac{1}{sin ( θ )} + 3

Is prove-(-1+sin^2(θ))/(sin^2(θ))=cot^2(θ) ?
The answer to whether prove-(-1+sin^2(θ))/(sin^2(θ))=cot^2(θ) is True