Question

tan⁴theta+tan²theta=sec⁴theta-sec²theta​

Answer 1

Step-by-step explanation:

LHS = Sec⁴theta - sec²theta = (1+tan²theta) ²-(1+tan²theta) = 1 +2tan²theta + tan⁴theta - 1-tan²theta

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

An equation involving trigonometry ratios of an angle is called is called a trigonometric identity, if it is true for all values of the angles involved. For any acute angle θ, we have 3 identities.

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

LHS = sec⁴ θ – sec²θ

LHS= sec² θ (sec² θ -1)

LHS= (1 + tan² θ) (1 + tan² θ -1)

[ sec² θ = 1 + tan² θ ]

LHS= (1 + tan² θ) ( tan² θ)

LHS= tan²θ + tan⁴θ

LHS = RHS

HOPE THIS WILL HELP u

We know that,

1 + tan²theta = sec²theta....

So,

LHS = Sec⁴theta -sec²theta

= (1+tan²theta) ²-(1+tan²theta)

= 1 +2tan²theta + tan⁴theta - 1-tan²theta

= tan⁴theta +tan²theta = RHS (Ans)

Answer 2

R.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