Question

find the value of 2 sin 15.cos 75​

Answer 1

Step-by-step explanation:

2-root3/2 is the value

Answer 2

$\red{ Value \: of \: 2 sin 15 \times cos 75 }\\= 2 sin 15 \times cos (90 - 15 ) \\= 2 sin 15 \times sin 15 \\= 2 sin^{2} 15$

$= 2 sin^{2} ( 45 - 30 )\\= 2 ( sin 45 cos 30 - sin 30 cos 45 )^{2} \\= 2 \Big( \frac{1}{\sqrt{2}} \times \frac{\sqrt{3}}{2} - \frac{1}{2} \times \frac{1}{\sqrt{2}} \Big)^{2}\\ = 2 \Big( \frac{\sqrt{3} - 1 }{ 2 \sqrt{2} }\Big)^{2} \\= 2 \times \frac{ (\sqrt{3})^{2} + 1^{2} - 2 \times \sqrt{3} \times 1 }{8} \\= \frac{ 3 + 1 - 2\sqrt{3}}{4} \\= \frac{ 4 - 2\sqrt{3}}{4} \\= \frac{2( 2 - \sqrt{3})}{4} \\= \frac{( 2 - \sqrt{3})}{2}$

Therefore.,

$\red{ Value \: of \: 2 sin 15 \times cos 75 }\\\green { = \frac{( 2 - \sqrt{3})}{2}}$

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