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If + cosec = 2, then the value of ^{8} + cosec ^{8} is

Question

If $sin θ + cosec θ = 2,$ then the value of $sin^{8} θ + cose c^{8} θ$ is equal to

2

2^{8}

2^{4}

none of these

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Eleanor Discussed

sin θ + cosec θ = 2,

then the value of

sin^{8} θ + cose c^{8} θ

is equal to

8 mins ago

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8 mins ago

Text solutionVerified

s in θ + cosec θ = 2 \Rightarrow s in θ + \frac{1}{s in θ} = 2

Squaring both sides

(s in θ + \frac{1}{s in θ})^{2} = 2^{2} \Rightarrow s in^{2} θ + \frac{1}{s in ^{2} θ} + 2 s in θ \frac{1}{s in θ} = 4 \Rightarrow s in^{2} θ + \frac{1}{s in ^{2} θ} = 2

Again squaring bot sides

(s in^{2} θ + \frac{1}{s in ^{2} θ})^{2} = 2^{2} \Rightarrow s in^{4} θ + \frac{1}{s in ^{4} θ} = 2

Similarly

s in^{8} θ + \frac{1}{s in ^{8} θ} = 2

\Rightarrow s in^{8} θ + cosec^{8} θ = 2

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Question Text	If $sin θ + cosec θ = 2,$ then the value of $sin^{8} θ + cose c^{8} θ$ is equal to
Answer Type	Text solution:1
Upvotes	150