Question

Solve: - (sin60° + cos30°) – (sin 30° + cos60°)​

Answer 1

$\mathbb{ANSWER:}$

$\boxed{0.5}$

Step-by-step explanation:

We know that, sin $60^o = \frac{\sqrt{3} }{2}$

$cos 30^o = \frac{\sqrt{3} }{2} \\\\sin30^o = \frac{1}{2} \\\\cos60^o = \frac{1}{2}$

Putting all values,

(sin60° + cos30°) – (sin 30° + cos60°)​

 $\Longrightarrow (\frac{\sqrt{3} }{2} + \frac{\sqrt{3} }{2}) -( \frac{1}{2} + \frac{1}{2} )\\\\\Longrightarrow \frac{\sqrt{3}+\sqrt{3} }{2 +2} -\frac{1}{2 \times2} \\\\\Longrightarrow\frac{3}{4} - \frac{1}{4}\\\\\Longrightarrow \frac{3-1}{4} \\\\\Longrightarrow \frac{2}{4} \\\\\Longrightarrow \frac{1}{2} (cancellation)\\\\\Longrightarrow 0.5$

$\bold{HENCE,}$ $\bold{(sin60^o + cos30^o) - (sin 30^o + cos60^o)}$ $=\boxed{ \bold{0.5}}$

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