Question

If 4cos square theta -1 =0 then cosec theta=

Answer 1

Correct Question

If 4cos²(θ) = -1 then cosec(θ) = ?

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Required Solution

We are given in this question that, 4cos²θ is equal to -1 and we need to find out the value of cosecθ, such that,

• 4cos²(θ) = -1
• cosec(θ) = ?

We know the trigonometric ratio of cos(θ) and cose(θ) is,

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• cos(θ) = b/h
• cosec(θ) = h/p

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We are given,

➙ 4cos²(θ) = -1

➙ cos²(θ) = -1/4

➙ cos(θ) = √(-1/4)

➙ cos(θ) = √-1/2 = b/h

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So, here the value of base is √-1 and the value of hypotenuse is 2 units.

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Now, we need to calculate the value of perpendicular. So by using the pythagoras theorem we can easily calculate the perpendicular.

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The formula of Pythagoras theorem is,

➙ (Hypotenuse)² = (Perpendicular)² + (Base)²

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By substituting all the given values in the formula, we get:

➙ (2)² = (P)² + (√-1)²

➙ 4 = (P)² + (-1)

➙ 4 = (P)² - 1

➙ 4 + 1 = P²

➙ 5 = P²

➙ √5 = P

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Now we have also the value perpendicular now we can easily find out the value of cosec(θ).

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We know that the trigonometric ratio of cose(θ) is,

cosec(θ) = h/p

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By using the trigonometric ratio and substituting their values in it, we get:

➙ cosec(θ) = 2/√5

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Hence, the required value of cosec(θ) is 2/√5.