Question

4 (sin (pi/2+x)+cos (pi+x)+sin (pi-x))/sin x

Answer 1

$\frac{4(sin(\pi/2 +x)+cos(pi+x)+sin(\pi -x))}{sinx} = \frac{4(cosx-cosx+sinx)}{sinx} =\frac{4sinx}{sinx} =4$

Answer 2

Let's simplify the expression step by step:

1. Start with the given expression:

   4 * [sin(pi/2 + x) + cos(pi + x) + sin(pi - x)] / sin(x)

2. Use trigonometric identities to simplify the trigonometric functions:

   • sin(pi/2 + x) = cos(x)
   • cos(pi + x) = -cos(x)
   • sin(pi - x) = sin(x)

   So, the expression becomes:

   4 * [cos(x) - cos(x) + sin(x)] / sin(x)

3. Now, combine like terms in the numerator:

   4 * [0 + sin(x)] / sin(x)

4. Simplify further:

   4 * sin(x) / sin(x)

5. Finally, cancel out the sin(x) terms:

   4

So, the simplified expression is 4.