would you mind if you write your complete solution?
Solve the simultaneous equations sin x. cos y = 1/4 & 3 tan x = tan y.
Ans: x = -π/6 + (k + l)π ; k,l belong to Z
y = 2π/3 + (k - l)π ; k, l belong to Z
The approach to the problem is very direct. There is no difficulty in solving it. However, there seems to be a conflict with the given answer and my answer. Solving, I got two equations: x + y = kπ + (-1)^k * π/2
x - y = lπ - (-1)^l * π/6
Proceeding further, my answers dont match with the given solutions.
Please help!!
I probably went a roundabout and tediously long way of finding this, but the idea here is to abuse substitution and take advantage of the identity ...
You have:
Notice that...
I guess that really didn't get us anywhere, did it?
Let's use the identity:
From , we have , so , and then
where
We had which can now simplify to just
Square both sides
Multiply by
Substitute
Let
Using the quadratic equation...
Solve for x.