First slide

Trigonometric equations

Question

$\cos^{2} u + \cos^{2} (u + x) - 2 \cos u \cos x \cos (u + x) = 1 / 2$ if

Moderate

A

$x = π / 4$
B

$u = π / 4$
C

$x = π / 2$
D

$u = π / 2$

Solution

L.H.S $= \cos^{2} u + \cos^{2} (u + x)$ $- [\cos (u + x) + \cos (u - x)] \cos (u + x)$
$\begin{array}{l} = \cos^{2} u - \cos (u - x) \cos (u + x) \\ = \cos^{2} u - (\cos^{2} u - \sin^{2} x) = \sin^{2} x \end{array}$
so $\sin^{2} x = 1 / 2 \Rightarrow \sin x = 1 / \sqrt{2}$

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