The value of the below expression istan 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 = 1/cot θ ∴ tan 1^∘. cot 1^∘.tan ...

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Standard X

Mathematics

Introduction to Trigonometry

The value of ...

Question

The value of the below expression is
$t a n 1^{\circ} . t a n 89^{\circ} . t a n 2^{\circ} . t a n 88^{\circ}$

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Solution

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

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Similar questions

Q. The value of the below expression is

t a n 1^{\circ} . t a n 89^{\circ} . t a n 2^{\circ} . t a n 88^{\circ}

Q. What is the value of the expression

tan 1^{\circ} tan 89^{\circ} . tan 2^{\circ} . tan 88^{\circ}

The value of the expression tan 1 ° \times tan 2 ° \times tan 3 ° \times . . . \times tan 89 ° is

$t a n 1^{\circ} . t a n 89^{\circ} = t a n 2^{\circ} . t a n 88^{\circ}$

The value of the expression tan 1 ° \times tan 2 ° \times tan 3 ° \times . . . \times tan 89 ° is

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The value of the below expression is tan 1∘.tan 89∘.tan 2∘.tan 88∘

The correct option is B 1The 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

The value of the below expression is
$t a n 1^{\circ} . t a n 89^{\circ} . t a n 2^{\circ} . t a n 88^{\circ}$