If A + B = 225∘, then cotA1+cotA. cotB1+cotB =

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Question

If A + B =

225^{\circ}

, then

\frac{c o t A}{1 + c o t A}

.

\frac{c o t B}{1 + c o t B}

=

Options:

A . 1

B . -1

C . 0

D . 12

Answer: Option D
:
D

\frac{c o t A}{1 + c o t A}

.

\frac{c o t B}{1 + c o t B}

=

\frac{1}{(1 + t a n A) (1 + t a n B)}

=

\frac{1}{t a n A + t a n B + 1 + t a n A t a n B}

[ ∵ tan(A + B) =

t a n 225^{\circ}

]

\Rightarrow

tanA + tan B = 1 - tan A tan B
=

\frac{1}{1 - t a n A t a n B + 1 + t a n A t a n B}

=

\frac{1}{2}

.

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