Prove the following. tan4q + tan2q = sec4q - sec2q
Chapter 6 – Trigonometry – Text Book Solution
Problem set 6| Q 5.5| Page 138
Prove the following.
(5) tan4q + tan2q = sec4q – sec2q
Solution
tan4θ + tan2θ
= tan2θ( tan2θ + 1)
= (sec2θ - 1)(sec2θ) [1 + tan2θ = sec2θ]
= sec4θ - sec2θ
= RHS
Solution
cot^2θ – tan^2θ
= (cosec^2θ – 1) – (sec^2θ – 1) ……(1)
[∵ 1 + tan^2θ = sec^2θ & 1 + cot^2θ = cosec^2θ]
= cosec^2θ – sec^2θ ……..(2)
Substituting (2) in (1), we get:
cot^2θ – tan^2θ = cosec^2θ – sec^2θ
Chapter 6 – Trigonometry – Text Book Solution
Problem Set 6 |Q 5.5| P 138
Click Here to see All the Textbook solution of Geometric Construction