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Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

MathematicsTrigonometric Ratios & IdentitiesAddition, Multiplication, Subtraction formula based,Multiple/Submultiple anglesMedium2 minPYQ_2017

MathematicsMediumsingle choice

If $5 (\tan^{2} x - \cos^{2} x) = 2 \cos 2 x + 9,$ then the value of $\cos 4 x$ is

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Answer:

Solution:

$5 (\frac{1 - \cos 2 x}{1 + \cos 2 x} - \frac{1 + \cos 2 x}{2}) = 2 \cos 2 x + 9$

Let, $\cos 2 x = y$

$∴ 5 (\frac{1 - y}{1 + y} - \frac{1 + y}{2}) = 2 y + 9$

$\Rightarrow 5 [- y^{2} - 4 y + 1] = 4 y^{2} + 22 y + 18$

$\Rightarrow 9 y^{2} + 42 y + 13 = 0$

$\Rightarrow y = - \frac{1}{3}$ or $y = - \frac{13}{3}$ (Not possible)

Now, $\cos 4 x = 2 \cos^{2} 2 x - 1$

$\Rightarrow \cos 4 x = 2 {(- \frac{1}{3})}^{2} - 1$

$\Rightarrow \cos 4 x = - \frac{7}{9}$

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

⏱ 2mℹ️ Source: PYQ_2017

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