First slide

Compound angles

Question

If $\sin α \sin β - \cos α \cos β + 1 = 0$ then $1 + \cot α \tan β =$

Moderate

A

-1
B

1
C

0
D

2

Solution

$\begin{array}{l} W e h a v e \sin α \sin β - \cos α \cos β = - 1 \\ \Rightarrow \cos (α + β) = 1 \Rightarrow α + β = 0, 2 π, 4 π \dots \dots \\ N o w 1 + \cot α \tan β = 1 + \frac{\cos α}{\sin α} \cdot \frac{\sin β}{\cos β} \\ = \frac{\sin (α + β)}{\sin α \sin β} \\ = 0 (∵ α + β = 2 n π) \end{array}$

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