Question

Question 3 (i)
Evaluate:
(i)$\frac{(si{n}^2{63}^{\circ }+si{n}^2{27}^{\circ })}{(co{s}^2{17}^{\circ }+co{s}^2{73}^{\circ })}$

Answer 1

(i) $\frac{(si{n}^2{63}^{\circ }+si{n}^2{27}^{\circ })}{(co{s}^2{17}^{\circ }+co{s}^2{73}^{\circ })}$
$=\frac{\left[si{n}^2\right({90}^{\circ }-{27}^{\circ })+si{n}^2{27}^{\circ }]}{\left[co{s}^2\right({90}^{\circ }-{73}^{\circ })+co{s}^2{73}^{\circ })]}$

Now, since $sin(90-\theta )=cos\theta$ and $cos(90-\theta )=sin\theta$

$=\frac{(co{s}^2{27}^{\circ }+si{n}^2{27}^{\circ })}{(si{n}^2{73}^{\circ }+co{s}^2{73}^{\circ })}$ $(\because si{n}^{2}A+co{s}^{2}A=1)$

$=\frac{1}{1}=1$