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Question: \[\cot(45{^\circ} + \theta)\cot(45{^\circ} - \theta) =\]...

cot⁡(45∘+θ)cot⁡(45∘−θ)=\cot(45{^\circ} + \theta)\cot(45{^\circ} - \theta) =

A

– 1

B

0

C

1

D

∞\infty

Answer

1

Explanation

Solution

cot⁡(45∘+θ)cot⁡(45∘−θ)=tan⁡(90∘−45∘−θ)cot⁡(45∘−θ)\cot(45{^\circ} + \theta)\cot(45{^\circ} - \theta) = \tan(90{^\circ} - 45{^\circ} - \theta)\cot(45{^\circ} - \theta)

=tan⁡(45∘−θ)cot⁡(45∘−θ)=1= \tan(45{^\circ} - \theta)\cot(45{^\circ} - \theta) = 1.