(45^ + ) (45^ - )= - Vidyadip

MCQ

$\cot\left(45^{\circ}+\theta\right)\cot\left(45^{\circ}-\theta\right)=$

A
-1
B
$0$
✓
1
D
$\infty$

✓

Answer

Correct option: C.

1

(C)
$\cot\left(45^{\circ}+\theta\right)\cot\left(45^{\circ}-\theta\right)$
$=\tan\left(90^{\circ}-45^{\circ}-\theta\right)\cot\left(45^{\circ} \theta\right)$
$\ldots\left[\because\tan\left(90^{\circ}-\theta\right)=\cot\theta\right]$
$=\tan\left(45^{\circ}-\theta\right)\cot\left(45^{\circ}-\theta\right)=1$

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