Question

$\cos( \alpha ) = \sin(150 - \alpha )$
Find the value of alpha.
​

Answer 1

$\red{QUESTION:-}$

$cos( \alpha ) = sin(150 - \alpha )$

$\red{ANSWER:-}$

$\implies \: cos( \alpha ) = sin(150 - \alpha ) \\ \implies \: sin( \frac{\pi}{2} - \alpha ) - sin(150 - \alpha ) \\ \implies \: sin( \frac{\pi}{2} - \alpha ) - sin(150 - \alpha ) \: = 0 \\ \implies \: 2cos( \frac{\pi - 4 \alpha + 300}{4} )sin( \frac{\pi - 300}{4} ) = 0 \\ \implies \: 2sin( \frac{\pi - 300}{4} )cos( \frac{\pi - 4a + 300}{4} ) = 0 \\ \implies \: cos( \frac{\pi - 4 \alpha + 300}{4}) = 0 \\ \implies \frac{\pi - 4 \alpha + 300}{4} = \frac{\pi}{2} + k\pi \: \:...... (k \: \epsilon \: z) \\ \implies\pi - 4 \alpha + 300 = 2\pi + 4k\pi.......(k \: \epsilon \: z) \\ \implies \: - 4 \alpha = 2\pi - \pi - 300 + 4k\pi.......(k \: \epsilon \: z) \\ \implies \: - 4 \alpha = \pi - 300 + 4k\pi.......(k \: \epsilon \: z) \\ \implies \: \red{\alpha = \frac{\pi}{4} + 75 + k\pi.......(k \: \epsilon \: z) }\:$

Answer 2

The value of alpha should be 60.

Explanation:

We are given that ,

$\cos (\alpha)=\sin (150^{\circ}-\alpha)$

Since we know that  , $\mathbf{\sin (90^{\circ}-x)=\cos x}$

$\\\\\Rightarrow\ \sin (90^{\circ})=\sin (150^{\circ}-\alpha)$

$\Rightarrow\ 90^{\circ}=150^{\circ}-\alpha\\\\\Rightarrow\ \alpha=150^{\circ}-90^{\circ}\ \ [\text{Subtract 90 from both sides}]\\\\\Rightarrow\mathbf{\alpha=60^{\circ}}$

Hence, the value of alpha should be 60.

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