Question : If $\cos A=\frac{1}{2}, 0 \leq A \leq 90^{\circ}$, then what is the value of sin (180 - A)?
Option 1: $\frac{1}{2}$
Option 2: $\frac{\sqrt{3}}{2}$
Option 3: $\frac{1}{\sqrt{3}}$
Option 4: $1$
Correct Answer: $\frac{\sqrt{3}}{2}$
Solution :
According to the question
sin
2
A + cos
2
A = 1
⇒ sin$^{2} A + \frac{1}{2}^{2}$ = 1
⇒ sin$^{2} A + \frac{1}{4}$ = 1
⇒ sin$^{2} A = 1 - \frac{1}{4}$ = $\frac{3}{4}$
⇒ Sin A = $\frac{\sqrt{3}}{2}$
Now,
⇒ sin(180 − A) = sin A = $\frac{\sqrt{3}}{2}$
Hence, the correct answer is $\frac{\sqrt{3}}{2}$
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