Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

MathematicsTrigonometric Ratios & IdentitiesAddition, Multiplication, Subtraction formula based,Multiple/Submultiple anglesEasy2 minPYQ_2021

MathematicsEasysingle choice

$cosec 18 °$ is a root of the equation:

Options:

Answer:

Solution:

We know that

$\sin 18 ° = \frac{\sqrt{5} - 1}{4}$

$cosec 18 ° = \frac{1}{\sin 18 °} = \frac{4}{\sqrt{5} - 1}$

Rationalizing denominator

$= \frac{4}{\sqrt{5} - 1} \times \frac{\sqrt{5} + 1}{\sqrt{5} + 1}$

$= \frac{4 (\sqrt{5} + 1)}{4}$

$= \sqrt{5} + 1$

Hence equation $x = \sqrt{5} + 1$

$\Rightarrow (x - 1)^{2} = 5$

$\Rightarrow x^{2} - 2 x + 1 = 5$
$\Rightarrow x^{2} - 2 x - 4 = 0$

Stream:JEESubject:MathematicsTopic:Trigonometric Ratios & IdentitiesSubtopic:Addition, Multiplication, Subtraction formula based,Multiple/Submultiple angles

⏱ 2mℹ️ Source: PYQ_2021

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