UPSKILL MATH PLUS
Learn Mathematics through our AI based learning portal with the support of our Academic Experts!
Learn moreVerify the following identities, where the angles involved are acute angles for which the expressions are defined.
\((cosec θ – cot θ)^2 = \frac{1 – cosθ}{1 + cosθ}\)
Explanation:
We know that, \(cosec \theta=\frac{1}{sin \theta}\) and \(cot \theta=\frac{cos \theta}{sin \theta}\)
Therefore, \((cosec θ – cot θ)^2\)=
[\(sin^2 \theta=1-cos^2 \theta\)]
Therefore, \((cosec \theta – cot \theta)^2\) =
\(= \frac{1-cos \theta}{1+cos \theta}\)
\(=\) RHS , Hence Proved.
Answer variants:
\(\frac{(1-cos\theta)^2}{(1-cos \theta)(1+cos \theta)}\)
\(= \frac{(1-cos \theta)^2}{(1-cos^2 \theta)}\)
\(= \frac{(1-cos \theta)^2}{sin^2\theta}\)
Register for free to see more content