show that :
tan3 theta/ 1+tan2 theta+ cot3 theta/ 1+cot2 theta= sec theta cosec theta - 2 sin theta cos theta
Answers
Answered by
26
Step-by-step explanation:
Given tan^3 theta/ 1+tan^2 theta+ cot^3 theta/ 1+cot^2 theta = sec theta cosec theta - 2 sin theta cos theta
- Given tan^3 theta / 1 + tan^2 theta + cot^3 theta / 1 + cot^2 theta
- We can write this as
- So sin^3 theta / cos^3 theta / sec^2 theta + cos^3 theta / sin^3 theta / cosec^2 theta
- So sin^3 theta / cos^3 theta / 1 / cos^2 theta + cos^3 theta / sin^3 theta / 1 / sin^2 theta
- So sin^3 theta x cos^2 theta / cos^3 theta + cos^3 theta x sin^2 theta / sin^3 theta
- So sin^3 theta / cos theta + cos^3 theta / sin theta
- Taking lcm we get
- So sin^4 theta + cos^4 theta / sin theta cos theta
- We can write this as
- sin^4 theta + cos^4 theta + 2 sin^2 theta cos^2 theta – 2 sin^2 theta cos^2 theta / sin theta cos theta
- So (sin^2 theta + cos^2 theta)^2 – 2 sin^2 theta cos^2 theta / sin theta cos theta
- 1 – 2 sin^2 theta cos^2 theta / sin theta cos theta
- So we can split and write this as
- 1 / sin theta cos theta – 2 sin^2 theta cos^2 theta / sin theta cos theta
- So sec theta cosec theta – 2 sin theta cos theta = Rhs (hence proved)
Reference link will be
https://brainly.in/question/9256121
Answered by
159
Answer:
Hope it helps u!!
Step-by-step explanation:
Please understand it 1st. Then write it in ur cw after understanding. Thank u☺☺
Attachments:
Similar questions