Question

Evaluate each of the following

$si{n}^2{30}^o+si{n}^2{45}^o+4ta{n}^2{30}^o+\frac{1}{2}si{n}^2{90}^o-2co{s}^2{90}^o+\frac{1}{24}co{s}^2{0}^o$

Answer 1

$si{n}^2{30}^o+si{n}^2{45}^o+4ta{n}^2{30}^o+\frac{1}{2}si{n}^2{90}^o-2co{s}^2{90}^o+\frac{1}{24}co{s}^2{0}^o$

=($\frac{1}{2}$)² + ($\frac{1}{\sqrt{2}}$)² + 4$\times (\frac{1}{\sqrt{3}}$)² + $\frac{1}{2}\times$1² - 2$\times$0 + $\frac{1}{24}\times$1

=$\frac{1}{4}$ + $\frac{1}{2}$ + $\frac{4}{3}$ + $\frac{1}{2}$ + $\frac{1}{24}$

=$\frac{63}{24}$