Question

$si{n}^{6}A+co{s}^{6}A+3si{n}^{2}Aco{s}^{2}A$ is equal to

• A. 3
• B. 2
• C. 1
• D. 0

Answer 1

Answer: (C)

$si{n}^{6}A+co{s}^{6}A+3si{n}^{2}Aco{s}^{2}A$
$={({\sin }^{2}A)}^3+{({\cos }^{2}A)}^3+3{\sin }^{2}A.{\cos }^{2}A$
$=({\sin }^{2}A+{\cos }^{2}A)({\sin }^{4}A.+{\cos }^{4}A$
$-{\sin }^{2}A{\cos }^{2}A)+3{\sin }^{2}A{\cos }^{2}A$
$={({\sin }^{2}A)}^2+{({\cos }^{2}A)}^2+2{\sin }^{2}A{\cos }^{2}A$
$={({\sin }^{2}A+{\cos }^{2}A)}^2=1$