Question

Find the value of the following:

sin² 30° – 2 cos³ 60° + 3 tan⁴ 45°

Answer 1

sin 30° = ${\displaystyle \frac{1}{2}}$, cos 60° = ${\displaystyle \frac{1}{2}}$, tan 45° = 1

sin² 30° – 2 cos³ 60° + 3 tan⁴ 45°

= ${\displaystyle {\left(\frac{1}{2}\right)}^2-2{\left(\frac{1}{2}\right)}^3+3{\left(1\right)}^4}$

= ${\displaystyle \left(\frac{1}{4}\right)-2\left(\frac{1}{8}\right)+3}$

= ${\displaystyle \left(\frac{1}{4}\right)-\left(\frac{1}{4}\right)+3}$

= 3