^6A+ ^6A+3 ^2A ^2A= - Vidyadip

MCQ

$\sin^6\text{A}+\cos^6\text{A}+3\sin^2\text{A}\cos^2\text{A}=$

A
$0$.
✓
$1.$
C
$2.$
D
$3$.

✓

Answer

Correct option: B.

$1.$

We have:
$\sin^6\text{A}+\cos^2\text{A}+3(\sin^2\text{A})(\cos^2\text{A})$
$=(\sin^2\text{A})^3+(\cos^2\text{A})^3+3(\sin^2\text{A})(\cos^2\text{A})\times1$
$=(\sin^2\text{A})^3+(\cos^2\text{A})^3+3(\sin^2\text{A})(\cos^2\text{A})(\sin^2\text{A}+\cos^2\text{A})$
$=(\sin^2\text{A}+\cos^2\text{A})^3$
$=1^3=1$

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