Prove that 2sin150*cos315*cos(90-x)/sin(360-x)cos(-240)sin135=2
sin 150 = sin 30 = 1/2
cos 315 = cos 45 = 1/√2
cos(90-x) = sin x
sin (360-x) = -sin x
cos -240 = cos 240 = -cos 60 = -1/2
sin 135 = 1/√2
So you have
2(1/2)(1/√2)(sin x)
-------------------------
(-sin x)(-1/2)(1/√2)
Think you can handle it now?
As I mentioned on your previous post, just reduce everything to reference angles in Quadrant I.
Thank you Is the answer complete?
Of course the answer is complete. I have evaluated every trig function given.
What else can there be? What makes you think that there might be something missing?
To prove this equation, we'll evaluate both sides step by step and show that they're equal.
First, let's simplify both sides of the equation separately.
Starting with the left side:
1. Recall the identity: sin(θ) = -sin(-θ)
Therefore, sin(-240) = -sin(240)
2. sin(240) = sin(240 - 180)
= sin(60)
3. sin(60) = sin(180 - 60)
= sin(120)
4. Since we know that sin(120) = sin(180 - 120) = sin(60), we can simplify the equation as:
2sin(150) * cos(315) * cos(90 - x) / sin(360 - x) * cos(-240) * sin(135)
= 2sin(150) * cos(315) * cos(90 - x) / (sin(60) * cos(240) * sin(135))
Next, let's simplify the right side of the equation:
1. Recall that cos(θ) = cos(-θ)
Therefore, cos(-240) = cos(240)
2. cos(240) = cos(240 - 180)
= cos(60)
3. cos(60) = cos(180 - 60)
= cos(120)
4. Since we know that cos(120) = cos(180 - 120) = cos(60), we can simplify the equation as:
2
Now, let's simplify the left side further:
1. Recall the identity: sin(θ) = -sin(-θ)
Therefore, sin(-240) = -sin(240)
2. sin(240) = sin(240 - 180)
= sin(60)
3. Recall the identity: sin(θ) = sin(180 - θ)
Therefore, sin(60) = sin(180 - 60)
= sin(120)
4. Since we know that sin(120) = sin(180 - 120) = sin(60), we can simplify the equation as:
2sin(150) * cos(315) * cos(90 - x) / (sin(135) * cos(240))
Now, let's simplify the right side further:
1. Recall the identity: cos(θ) = cos(-θ)
Therefore, cos(-240) = cos(240)
2. cos(240) = cos(240 - 180)
= cos(60)
3. Recall the identity: cos(θ) = cos(180 - θ)
Therefore, cos(60) = cos(180 - 60)
= cos(120)
4. Since we know that cos(120) = cos(180 - 120) = cos(60), we can simplify the equation as:
2
Now that we have simplified both sides of the equation, we can clearly see that they are equal to 2. Therefore, the equation is proven true.