What is the value of the expression tan 1-tan 89-tan 2- tan 88-

The given expression is tan 1^∘. tan 89^∘.tan 2^∘. tan 88^∘ ∵tan θ = cot (90 θ) ⇒tan 1^∘. 1^∘.tan 2^∘. 2^∘ ∵tan θ = 1/ θ ∴tan 1^∘. 1^∘.tan 2^∘. 2^∘ = nbsp ...

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Standard X

Mathematics

Standard Values of Trigonometric Ratios

What is the v...

Question

What is the value of the expression $tan 1^{\circ} tan 89^{\circ} . tan 2^{\circ} . tan 88^{\circ}$ ?

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Solution

The given expression is
$tan 1^{\circ} . tan 89^{\circ} . tan 2^{\circ} . tan 88^{\circ}$
$∵ tan θ = c o t (90 - θ)$
$\Rightarrow tan 1^{\circ} . cot 1^{\circ} . tan 2^{\circ} . cot 2^{\circ}$
$∵ tan θ = \frac{1}{cot θ}$
$∴ tan 1^{\circ} . cot 1^{\circ} . tan 2^{\circ} . cot 2^{\circ} = 1$

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What is the value of the expression tan 1∘tan 89∘.tan 2∘.tan 88∘?

The given expression is tan 1∘.tan 89∘.tan 2∘.tan 88∘ ∵tan θ=cot(90−θ) ⇒tan 1∘.cot 1∘.tan 2∘.cot 2∘ ∵tan θ=1cot θ ∴tan 1∘.cot 1∘.tan 2∘.cot 2∘=1

What is the value of the expression $tan 1^{\circ} tan 89^{\circ} . tan 2^{\circ} . tan 88^{\circ}$ ?