If $sin (x - 20)^{o} = cos (3 x - 10)^{o}$ then find the value of $x$ .

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Solution

$sin (x - 20^{\circ}) = cos (3 x - 10^{\circ})$
$\Rightarrow sin (x - 20^{\circ}) = sin (90^{\circ} - (3 x - 10^{\circ}))$ since $sin (90^{\circ} - θ) = cos θ$
$\Rightarrow x - 20^{\circ} = 90^{\circ} - (3 x - 10^{\circ})$
$\Rightarrow x - 20^{\circ} = 90^{\circ} - 3 x + 10^{\circ}$
$\Rightarrow x + 3 x = 100^{\circ} + 20^{\circ} = 120^{\circ}$
$\Rightarrow 4 x = 120^{\circ}$
$∴ x = \frac{120^{\circ}}{4} = 30^{\circ}$

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