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C2: Please Help

Two trig questions:

1. Given that 2(sinx+2cosx) = sinx + 5cosx, find the exact value of tanx.

This is what I did:

2sinx + 4cosx = sinx + 5 cosx

sinx = cosx

(sinx)/(cosx) = 0

tanx = 0

x = 0

but answer is x = 1

2. Give that sinxcosy + 3cosxsiny = 2sinxsiny - 4cosxcosy, express tany in terms of tanx.

No clue...

Sol: tany = (4+tanx)/(2tanx - 3)

Thanks mathematicians.

Reply 1

BCHL85

blah888

sinx = cosx

(sinx)/(cosx) = 0

tanx = 0

Oh dear, sinx - cosx = 0, and sinx/cosx = 1 (not 0).
So tanx = 1 -> x = pi/4
I don't know why the answer is 1.

2. Give that sinxcosy + 3cosxsiny = 2sinxsiny - 4cosxcosy, express tany in terms of tanx.

No clue...

Sol: tany = (4+tanx)/(2tanx - 3)

Thanks mathematicians.

Put siny in 1 side, cosy in the other one.
3cosxsiny - 2 sinxsiny = -4cosxcosy - sinxcosy
siny(3cosx-2sinx) = -cosy(4cosx +sinx)
-> siny/cosy = (4cosx + sinx)/(2sinx-3cosx)
Now devide the RHS by cosx
Is it ok now?