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

Trigonometry Practice Test 1

Question : 3 of 40

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

\sin^4 θ + \cos^4 θ

Solution:

\sin θ + \cosec θ = 2

⇒\sinθ+1/{\sinθ}=2

⇒\sin^2θ-2\sinθ+1=0

⇒(\sinθ-1)^2=0⇒\sinθ=1

⇒\sinθ=\sin90°⇒θ=90°

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

=1+0=1

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