Tan 1-tan 89-tan 2-tan 88-

The correct option is A True tan1^∘.tan89^∘ = tan1^∘.cot(90^∘ 89^∘) = tan1^∘. cot1^∘ = 1 (Since tanθ.cotθ = 1) Similarly, tan2^∘.tan88^∘ = tan2^∘.cot(90^∘ ...

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Byju's Answer

Standard IX

Mathematics

Complementary Ratios

tan 1∘·tan 89...

Question

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

True

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False

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Solution

The correct option is A
True

$t a n 1^{\circ} . t a n 89^{\circ}$
$= t a n 1^{\circ} . c o t (90^{\circ} - 89^{\circ})$
$= t a n 1^{\circ} . c o t 1^{\circ}$
$= 1$ ( $S i n c e t a n θ . c o t θ = 1$ )
Similarly,
$t a n 2^{\circ} . t a n 88^{\circ}$
$= t a n 2^{\circ} . c o t (90^{\circ} - 88^{\circ})$
$= t a n 2^{\circ} . c o t 2^{\circ} = 1$
$\Rightarrow t a n 1^{\circ} . t a n 89^{\circ} = t a n 2^{\circ} . t a n 88^{\circ}$

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Similar questions

S t a t e t r u e o r f a l s e .

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

P-1:-tan1.tan2.tan3......tan87.tan88.tan89=1

t a n 1^{\circ} . t a n 2^{\circ} . t a n 3^{\circ} . . . t a n 89^{\circ}

=_________.

tan 1^{\circ} tan 2^{\circ} tan 3^{\circ} . . . . . . . . . . . tan 89^{\circ} =

tan 1^{\circ} tan 2^{\circ} tan 3^{\circ} . . . tan 89^{\circ} =

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tan1∘.tan89∘=tan2∘.tan88∘

The correct option is A True tan1∘.tan89∘ =tan1∘.cot(90∘−89∘) =tan1∘. cot1∘ =1 (Since tanθ.cotθ=1) Similarly, tan2∘.tan88∘ =tan2∘.cot(90∘−88∘) =tan2∘.cot2∘=1 ⇒tan1∘.tan89∘=tan2∘.tan88∘

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