The value of cos 3 π 8 . cos 3 π 8 + sin 3 π 8 . sin 3 π 8 is:

⇒ cos 3 π 8 cos π 2 - π 8 + sin 3 π 8 sin π 2 - π 8 ⇒ cos 3 π 8 sin π 8 + sin 3 π 8 cos π 8 ⇒ sin π 8 cos π 8 sin 2 π 8 + cos 2 π 8 ⇒ 1 2 sin π 4 ⇒ 1 2 2

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Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

MathematicsTrigonometric Ratios & IdentitiesAddition, Multiplication, Subtraction formula based,Multiple/Submultiple anglesMedium2 minPYQ_2020

MathematicsMediumsingle choice

The value of $\cos^{3} (\frac{π}{8}) . \cos (\frac{3 π}{8}) + \sin^{3} (\frac{π}{8}) . \sin (\frac{3 π}{8})$ is:

Options:

Answer:

Solution:

$\Rightarrow \cos^{3} (\frac{π}{8}) \cos (\frac{π}{2} - \frac{π}{8}) + \sin^{3} (\frac{π}{8}) \sin (\frac{π}{2} - \frac{π}{8})$

$\Rightarrow \cos^{3} \frac{π}{8} \sin \frac{π}{8} + \sin^{3} \frac{π}{8} \cos \frac{π}{8}$

$\Rightarrow \sin \frac{π}{8} \cos \frac{π}{8} (\sin^{2} \frac{π}{8} + \cos^{2} \frac{π}{8})$

$\Rightarrow \frac{1}{2} \sin \frac{π}{4}$

$\Rightarrow \frac{1}{2 \sqrt{2}}$

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

⏱ 2mℹ️ Source: PYQ_2020

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