Find the value of : cos75.sin75

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Solution

sin 75 cos 75 = A
Multiplying both side by 2
$∴$ 2 sin 75 cos 75 = 2A
$\Rightarrow$ sin 150 = 2A
$\Rightarrow$ sin (180-30) = 2A
$\Rightarrow$ sin 30 = 2A
$\Rightarrow A = \frac{1}{4}$ .

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