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State the following statement is true or false cosec = {1 +

Question

State the following statement is true or false
$cosec θ = 1 + cot^{2} θ$

True

False

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State the following statement is true or false

cosec θ = 1 + cot^{2} θ

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Text solutionVerified

We know that

cot θ = \frac{cos θ}{sin θ}

csc θ = 1 + \frac{cos ^{2} θ}{sin ^{2} θ} = \frac{sin ^{2} θ + cos ^{2} θ}{sin ^{2} θ}

sin^{2} θ + cos^{2} θ = 1

\frac{sin ^{2} θ + cos ^{2} θ}{sin ^{2} θ} = \frac{1}{sin ^{2} θ} = \frac{1}{sin θ} = csc θ

Hence proved

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Question Text	State the following statement is true or false $cosec θ = 1 + cot^{2} θ$
Answer Type	Text solution:1
Upvotes	150