Question

$si{n}^{6}A+co{s}^{6}A+3si{n}^{2}Aco{s}^{2}A=$

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

The correct option is B

1

1

We have:

$si{n}^{6}A+co{s}^{6}A+3\left(si{n}^{2}A\right)\left(co{s}^{2}A\right)$

$=(si{n}^{6}A{)}^3+(co{s}^{2}A{)}^3+3\left(si{n}^{2}A\right)\left(co{s}^{2}A\right)\times 1$

$=(si{n}^{2}A{)}^3+(co{s}^{2}A{)}^3+3\left(si{n}^{2}A\right)\left(co{s}^{2}A\right)(si{n}^{2}A+co{s}^{2}A)$

$=(si{n}^{2}A+co{s}^{2}A)$

$=1^3=1$