If A + B = 225 ∘ , then c o t A 1 + c o t A . c o t B 1 + c o t B = Options: A . &nbsp 1 B . &nbsp -1 C . &nbsp 0 D . &nbsp 1 2

Answer: Option D : D c o t A 1 + c o t A . c o t B 1 + c o t B = 1 ( 1 + t a n A ) ( 1 + t a n B ) = 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 ∘ ] ⇒ tanA + tan B = 1 - tan A tan B = 1 1 − t a n A t a n B + 1 + t a n A t a n B = 1 2 .

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

Discussion Forum : Trigonometric Functions

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 .

\frac{1}{2}

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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Discussion Forum : Trigonometric Functions

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