Question

If sin+cos=2; find the value of sin2cos2

Answer 1

Answer:

$\frac{9}{4}$

Step-by-step explanation:

$sin + cos = 2 \\ squaring \: on \: both \: sides \\ { (sin + cos)}^{2} = {2}^{2} \\ {sin}^{2} + {cos}^{2} + 2sin \times cos = 4 \\ 1 + 2sin \times cos = 4 \\ 2sin \times cos = 3 \\ sin \times cos = \frac{3}{2} \\ squaring \: on \: both \: sides \\ {sin}^{2} \times {cos}^{2} = \frac{9}{4}$

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