$tan 27^{o} tan 32^{o} + tan 32^{o} tan 31^{o} + tan 31^{o} tan 27^{o} =$

1

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Solution

The correct option is D $1$
Note that : 27 + 32 + 31 = 90, we are dealing with the form
S = tanA . tanB + tanB . tanC + tanC . tanA
or S = tanA. tanB + tanB. tan C (tanA + tanB)----(1)
A + B + C = 90
C = 90 - (A + B)
$∴$ tan C = tan(90-(A+B))
tan C = cot(A+B)
$= \frac{1}{t a n (A + B)}$
$∴ t a n C = \frac{1 - t a n A . t a n B}{t a n A + t a n B}$
$∴ t a n C (t a n A + t a n B) = - 1 t a n A . t a n B - - - - (i i)$
using (ii) in (i)
S = tanA. tanB + 1 - tanA. tanB
$∴$ S = 1

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Question 22

Which of the following is an example of distributive property of multiplication over addition for rational numbers.
(a) $- \frac{1}{4} \times {\frac{2}{3} + (\frac{- 4}{7})} = [- \frac{1}{4} \times \frac{2}{3}] + [- \frac{1}{4} \times (\frac{- 4}{7})]$
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