Question

Evaluate the following:

sin 30° + cos 45° + tan 180°

Answer 1

We know that,

sin 30° = ${\displaystyle \frac{1}{2}}$, cos 45° = ${\displaystyle \frac{1}{\sqrt{2}}}$, tan 180° = 0

sin 30° + cos 45° + tan 180°

= ${\displaystyle \frac{1}{2}+\frac{1}{\sqrt{2}}+0}$

= ${\displaystyle \frac{1}{2}+\frac{1}{\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}}}$           ...[Multiply numerator and denominator by ${\displaystyle \sqrt{2}}$]

= ${\displaystyle \frac{1}{2}+\frac{\sqrt{2}}{2}}$

= ${\displaystyle \frac{1+\sqrt{2}}{2}}$