Question

Sin50-cos320/2sin25*cos25

Answer 1

$\frac{sin50-cos320}{2sin25\cdot cos25}=[ \, cos320=cos(270+50)=sin50\, ]=\\\\= \frac{sin50-sin50}{sin50}=0$

Answer 2

To simplify the expression (sin50 - cos320) / (2sin25cos25), you can use trigonometric identities to rewrite the terms. First, let's simplify the numerator and denominator separately.

1. For the numerator: sin(50°) - cos(320°)

Use the periodicity of trigonometric functions: sin(50°) = sin(50° - 360°) = sin(-310°)

Now, use the co-function identity: sin(-x) = -sin(x)

So, sin(-310°) = -sin(310°)

Now, we have: Numerator: -sin(310°)

2. For the denominator: 2sin(25°)cos(25°)

Use the double-angle identity: sin(2x) = 2sin(x)cos(x)

So, 2sin(25°)cos(25°) = sin(2 * 25°) = sin(50°)

Now, we have: Denominator: sin(50°)

Now, the expression becomes: (-sin(310°)) / sin(50°)

Since sin(-x) = -sin(x), you can further simplify this as:

-(sin(310°) / sin(50°))

Now, if you want to find the numerical value of this expression:

sin(310°) is the same as sin(310° - 360°), which is sin(-50°). So,

-(sin(-50°) / sin(50°))

Use the property that sin(-x) = -sin(x):

-(-sin(50°) / sin(50°))

The negative signs cancel out:

sin(50°) / sin(50°) = 1

So, the simplified value of the expression is 1.