Question

38*sin50/sin65*sin25

Answer 1

В знаменателе применим формулу перехода от произведения к сумме, а в числителе формулу приведения.

$\dfrac{38\sin50^\circ}{\sin65^\circ\sin25^\circ}=\dfrac{38\sin(90^\circ-40^\circ)}{\frac{1}{2}\Big(\cos(65^\circ-25^\circ)-\cos(65^\circ+25^\circ)\Big)}=\dfrac{76\cos40^\circ}{\cos40^\circ-\cos90^\circ}=\\ \\ \\ =\dfrac{76\cos40^\circ}{\cos40^\circ-0}=\dfrac{76\cos40^\circ}{\cos40^\circ}=76$

Answer 2

To calculate the value of the expression (38 * sin(50)) / (sin(65) * sin(25)), we'll need to use a calculator or a mathematical software. However, I can provide you with the steps to solve it:

1. Convert the angles from degrees to radians, as the trigonometric functions in most mathematical libraries and calculators work with radians. Multiply the angles by π/180 to convert them.

   sin(50°) = sin(50 * π/180) sin(65°) = sin(65 * π/180) sin(25°) = sin(25 * π/180)

2. Calculate the values of sin(50 * π/180), sin(65 * π/180), and sin(25 * π/180) using a calculator or a mathematical software.

3. Substitute the calculated values into the expression:

   (38 * sin(50 * π/180)) / (sin(65 * π/180) * sin(25 * π/180))

The result will be the value of the expression. Remember to use a calculator or mathematical software that can handle trigonometric functions in radians for accurate calculations.