Plzz help find value of following : 2sin75°.cos15°

Mathematics

1 answer:

polet [3.4K]2 years ago

6 0

Answer:

$\frac{2+\sqrt{3} }{2}$

Step-by-step explanation:

Using the product to sum formula

sinxcosy = $\frac{1}{2}$ [ sin(x + y) + sin(x - y) ] , then

2sinxcosy = sin(x + y) + sin(x - y)

Given

2sin75°cos15° ← with x = 75 and y = 15 , then

= sin(75 + 15) + sin(75 - 15)

= sin90° + sin60°

= 1 + $\frac{\sqrt{3} }{2}$

= $\frac{2+\sqrt{3} }{2}$

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