Question

proof that:-
tan4theta+tan2theta=sec4theta-sec2theta​

Answer 1

Answer:

proof that:-

tan4theta+tan2theta=sec4theta-sec2theta

Answer 2

Step-by-step explanation:

tan^4\ \theta + tan^2\ \theta = sec^4\ \theta -sec^2\ \thetatan

4

θ+tan

2

θ=sec

4

θ−sec

2

θ

Solution:

Given that,

We have to prove:

tan^4\ \theta + tan^2\ \theta = sec^4\ \theta -sec^2\ \thetatan

4

θ+tan

2

θ=sec

4

θ−sec

2

θ

Take the LHS

tan^4\ \theta + tan^2\ \thetatan

4

θ+tan

2

θ

Take\ tan^2\ \theta\ as\ commonTake tan

2

θ as common

tan^2\theta(1+tan^2\ \theta)tan

2

θ(1+tan

2

θ) ---------- (1 )

We know that,

1+tan^2\ \theta = sec^2\ \theta1+tan

2

θ=sec

2

θ

Therefore, ( 1 ) becomes,

(sec^2 \theta - 1)(sec^2 \theta)(sec

2

θ−1)(sec

2

θ)

sec^4\ \theta - sec^2 \thetasec

4

θ−sec

2

θ

Thus,

LHS = RHS

Thus proved

Learn more about this topic

Prove that sec4 - sec2 = tan2 + tan4

https://brainly.in/question/741612

Show that tan4 theta + tan 2 theta = sec 4 theta minus sec 2 theta

https://brainly.in/question/9598400