Question

Prove the following identities sec⁴ 0 - tan⁴ 0 =sec² 0 + tan² 0​

Answer 1

Answer:

What is the proof of tan⁴ θ + tan² θ = sec⁴ θ - sec² θ?

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Trigonometry is the study of the relationship between the sides and angles of a triangle.

We know that :

i) sin² θ + cos² θ = 1 , ii) 1 + tan² θ = sec² θ , iii) cot² θ +1 = cosec² θ.

SOLUTION :

Given :

sec⁴ θ – sec²θ = tan⁴θ + tan²θ

L.H.S

= sec⁴ θ – sec²θ

= sec² θ (sec² θ -1)

= (1 + tan² θ) (1 + tan² θ -1) …..[ sec² θ = 1 + tan² θ ]

= (1 + tan² θ) ( tan² θ)

= tan²θ + tan⁴θ

L.H.S = R.H.S

I hope you got your answer……

Answer 2

First interchange the value of question to make secO one side and tanO one side.