Question

Find the value of the product. 2 sin(52.5°) sin(97.5°)

Answer 1

Answer:

2sin(52.5)sin(97.5)   = [√(2) + √(3)] /2

                                        =1.5731

Step-by-step explanation:

As we the trigonometric identity of the product of sines

sin(x)sin(y) =[cos(x-y) - cos(x+y)] /2

2sin(x)sin(y) =[cos(x-y) - cos(x+y)]  

putting values of x and y

2sin(52.5)sin(97.5) =[cos(52.5-97.5) - cos(52.5+97.5)]

                                      =cos(45)-cos(150)

                                      = 1/√(2) - (-√(3) /2)

                                      = √(2)/2  + √(3) /2)

                                      = [√(2) + √(3)] /2

                                       =1.5731

Answer 2

The value of the product 2 sin(52.5°) sin(97.5°) is 1.57.

What is sin identity?

The sin identity can be expressed as;

$\rm 2sin(x)sin(y) =cos(x-y) - cos(x+y)\\\\ sin(x)sin(y) =\dfrac{[cos(x-y) - cos(x+y)] }{2}$

Given

The product of the 2sin(52.5°) sin(97.5°).

By applying the sin identity

$\rm 2sin(52.5)sin(97.5) =[cos(52.5-97.5) - cos(52.5+97.5)]\\\\ 2sin(52.5)sin(97.5) =cos(45)-cos(150)\\\\ 2sin(52.5)sin(97.5) = \dfrac{1}{\sqrt{2} } - \left ( \dfrac{-\sqrt{3} }{2} \right )\\\\ 2sin(52.5)sin(97.5) = \dfrac{\sqrt{2} +\sqrt{3} }{2}\\\\2sin(52.5)sin(97.5) = 1.57$

Hence, the value of the product 2 sin(52.5°) sin(97.5°) is 1.57.

To know more about sin identity click the link given below.

https://brainly.com/question/13721232