Question

If A = ${60}^o$ and B = ${30}^o$, find the value of
$(sinA.cosB+cosA.sinB{)}^2$ + $(cosA.cosB-sinA.sinB{)}^2$.

• A. 0
• B. -1
• C. 1
• D. 2

Answer 1

The correct option is C

1

Given: A = ${60}^o$ and B = ${30}^o$

$(sinA.cosB+cosA.sinB{)}^2$ + $(cosA.cosB-sinA.sinB{)}^2$

$=(sin{60}^o.cos{30}^o+cos{60}^o.sin{30}^o{)}^2+$
$(cos{60}^o.cos{30}^o-sin{60}^o.sin{30}^o{)}^2$

$=\left[\right(\frac{\sqrt{3}}{2}\times \frac{\sqrt{3}}{2})+(\frac{1}{2}\times \frac{1}{2}){]}^2+$
$\left[\right(\frac{1}{2}\times \frac{\sqrt{3}}{2})-(\frac{\sqrt{3}}{2}\times \frac{1}{2}){]}^2$

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

$=\left[\right(\frac{3}{4})+(\frac{1}{4}){]}^2+0$

= $1^2=1$