First slide

Compound angles

Question

If $\frac{\cos (x - y)}{\cos (x + y)} + \frac{\cos (z + t)}{\cos (z - t)} = 0,$ hen the value of expression tanx tany tanz tant is equal to

Moderate

A

1
B

-1
C

2
D

-2

Solution

$\begin{array}{l} \frac{\cos (x - y)}{\cos (x + y)} + \frac{\cos (z + t)}{\cos (z - t)} = 0 \\ or \frac{1 + \tan xtan y}{1 - \tan xtan y} + \frac{1 - \tan ztan t}{1 + \tan ztan t} = 0 \\ or 1 + \tan ztan t + \tan xtan y + \tan xtan ytan ztan t + 1 - \tan ztan t - \tan xtan y + \tan xtan ytan ztan t = 0 \\ or \tan xtan ytan ztan t = - 1 \end{array}$

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