If tan 1 ∘ tan 2 ∘ ⋯ tan 8 9 ∘ = x 2 − 8 , then the value of x can be

x 2 − 8 = ( tan 1 ∘ tan 8 9 ∘ ) ( tan 2 ∘ tan 8 8 ∘ ) ⋯ ( tan 4 4 ∘ tan 4 6 ∘ ) tan 4 5 ∘ = ( tan 1 ∘ cot 1 ∘ ) ⋯ ( tan 4 4 ∘ cot 4 4 ∘ ) tan 4 5 ∘ = 1 ⇒ x 2 = 9 ⇒ x = ± 3

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Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

MathematicsTrigonometric Ratios & IdentitiesMiscellaneous/MixedMedium2 minQB

MathematicsMediummultiple choice

If $tan 1^{\circ} tan 2^{\circ} \dots tan 8 9^{\circ} = x^{2} - 8$ , then the value of $x$ can be

Options:(select one or more)

Answer:

C, D

Solution:

$x^{2} - 8 = (tan 1^{\circ} tan 8 9^{\circ}) (tan 2^{\circ} tan 8 8^{\circ}) \dots (tan 4 4^{\circ} tan 4 6^{\circ}) tan 4 5^{\circ} = (tan 1^{\circ} cot 1^{\circ}) \dots (tan 4 4^{\circ} cot 4 4^{\circ}) tan 4 5^{\circ} = 1$ $\Rightarrow x^{2} = 9 \Rightarrow x = \pm 3$

Stream:JEESubject:MathematicsTopic:Trigonometric Ratios & IdentitiesSubtopic:Miscellaneous/Mixed

⏱ 2mℹ️ Source: QB

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