If (m+2)sin ø + (2m-1)cos ø = 2m+1 then tan ø is equal to
using x to avoid copy/paste of ø,
m sinx + 2sinx + 2m cosx - cos x = 2m+1
(sinx + 2cosx)m + (2sinx - cosx) = 2m+1
If these are identical, then
sinx + 2cosx = 2
2sinx - cosx = 1
sinx = 4/5
cosx = 3/5
tanx = 4/3
Please explain clearly
Don't get confused by the statement - "if both sides are identical".. He is just comparing both the sides.
To find the value of tan ø, we need to rearrange the given equation in terms of sin ø and cos ø.
Let's start by simplifying the equation:
(m+2)sin ø + (2m-1)cos ø = 2m+1
Expanding the left side of the equation:
m sin ø + 2 sin ø + 2m cos ø - cos ø = 2m + 1
Rearranging the equation:
m sin ø + 2m cos ø + 2 sin ø - cos ø = 2m + 1
Next, we notice that m sin ø + 2m cos ø can be written using the identity sin(A + B) = sin A cos B + cos A sin B. We can rewrite the equation as follows:
sin ø (m + 2m) + cos ø (-1 + 2) = 2m + 1
3m sin ø + cos ø - 1 = 2m + 1
Now, let's isolate the terms containing sin ø and cos ø:
3m sin ø - 2m = 2 - cos ø
(3m - 2m) sin ø = 2 - cos ø
m sin ø = 2 - cos ø
Finally, we can find tan ø by dividing sin ø by cos ø:
tan ø = sin ø / cos ø
To get the value of tan ø, we can divide m sin ø by m cos ø:
tan ø = (2 - cos ø) / (m sin ø)
Therefore, tan ø is equal to (2 - cos ø) divided by (m sin ø).