Question

Evaluate
$1)$ $\frac{si{n}^2{63}^o+si{n}^2{27}^o}{co{s}^2{17}^o+co{s}^2{73}^o}$
$2)$ $sin{25}^{o}cos{65}^o+cos{25}^{o}sin{65}^o$

Answer 1

Given

$\frac{si{n}^{2}63+si{n}^{2}27}{co{s}^{2}17+co{s}^{2}73};sin{25}^{\circ }cos{65}^{\circ }+cos{25}^{\circ }sin{65}^{\circ }$

for $\theta$ $sin\theta =cos(90-\theta )$

$si{n}^2\theta +co{s}^2\theta =1$

$cos\theta =sin(90-\theta )$

$\frac{si{n}^{2}63+si{n}^2(90-27)}{co{s}^{2}17+co{s}^2(90-17)}$

$=\frac{si{n}^{2}63+co{s}^{2}63}{co{s}^{2}17+si{n}^{2}17}$

$=\frac{1}{1}$

$=1$

$sin25cos(90-{25}^{\circ })$

$+cos25sin(90-25)$

$=si{n}^{2}25+co{s}^{2}25$

$=1$