Question

If sec²theta+tan²theta = 13/12, then sec⁴theta =?

(A) 144/576
(B) 169/576
(C) 576/625
(D) 625/576



Please answer this question with steps.

Answer 1

⭐⭐⭐⭐⭐ ANSWER ⭐⭐⭐⭐⭐

Let "theta" be "x''.

Given, sec²x + tan²x = 13/12
Also, sec²x-tan²x = 1

Thus, on going through elimination method, we get :-

2 sec²x = 25/12
=> sec²x = 25/24
=> (sec²x)² = (25/24)²
=> sec⁴x = 625/576 [OPTION D]

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⭐⭐⭐ ALWAYS BE BRAINLY ⭐⭐⭐

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Answer 2

sec² θ + tan² θ = 13/12 .........................(1)

We know that :

sec² θ - tan² θ = 1 .....................(2)

Adding (1) and (2) :

2 sec ² θ = 13/12 + 1

==> 2 sec² θ = ( 13 + 12) / 12

==> 2 sec² θ = 25/12

==> sec² θ = 25/24

Squaring both sides we get :

==> sec⁴  θ = (25²)/(24²)

                   ==> 625/576

ANSWER:

$\boxed{\bf{OPTION\:\:D}}$

Hope it helps ya :)

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