98.1k views
9 votes
9.
(1 + tan²theta) cot theta
cosec theta
tan theta​

User Prelic
by
7.2k points

1 Answer

10 votes

Answer:

Proved

Step-by-step explanation:

Given


((1+tan^2\theta). cot\theta)/(cosec^2 \theta)= tan \theta

Required

Prove

In trigonometry:


1 + tan^2\theta = sec^2\theta

So, we have:


(sec^2\theta * cot\theta)/(cosec^2 \theta)= tan \theta

Express each identity as an inverse:


((1)/(cos^2\theta) * (1)/(tan\theta))/((1)/(sin^2 \theta))= tan \theta

Rewrite as:


((1)/(cos^2\theta) * (1)/(tan\theta))/ (1)/(sin^2 \theta)= tan \theta

Express tan as sin/cos:


((1)/(cos^2\theta) * (1)/(sin\theta/cos\theta))/ (1)/(sin^2 \theta)= tan \theta


((1)/(cos^2\theta) * (1)/(sin\theta/cos\theta)) * sin^2 \theta= tan \theta


((1)/(cos^2\theta) * (cos\theta)/(sin\theta)) * sin^2 \theta= tan \theta


((1)/(cos\theta) * (1)/(sin\theta)) * sin^2 \theta= tan \theta


(sin^2 \theta)/(cos\theta*sin\theta)= tan \theta


(sin \theta)/(cos\theta)= tan \theta


tan \theta= tan \theta

Proved

User Igon
by
7.0k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.