If sin θ+ cosecθ = 2, then what is the value of \sin^4 \theta+ \cos^4 \theta?

RRB NTPC Mains or Stage 2 Model Paper 5 with solutions

Question : 19 of 120

Marks: +1, -0

If sin θ+ cosecθ = 2, then what is the value of

sin^4 θ+ cos^4 θ?

Solution:

(d) sin θ + cosec θ = 2
⇒ sin θ +

1/sin θ = 2

⇒sin^2 θ– 2 sin θ + 1 = 0

⇒ (sin θ – 1)^2 = 0

⇒ sin θ = 1
⇒sin θ = sin 90°
⇒ θ= 90°
∴

sin^4 θ + cos^4 θ = sin^4 90° + cos^4 90°

= 1 + 0 = 1

Alternate Method
Giventhat
sinθ+ cosecθ = 2
Now, put – θ = 90°
1 + 1 = 2
Similary put θ = –90°

sin^4θ + cos^4θ

= sin^4 90 + cos^4 90°

= 1 + 0 = 1

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