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and 30° + 60° = 90°.
In the OP’s example, 0 < x < 90°, so 0 < (2x + 5) + (x − 5) = 3x < 270° ⇒ x = 90°.
PS: Check: tan(175°) = 1/tan(95°) so I think I’m on the right track.
]]>Sorry my post was too brief. I was in a hurry as I had to go out. Here's some more detail:
note:
Let A = 2x-5 and B = x+5 => A-B = x - 10 and A+B = 3x
The two trig. formulas that will help are
and
so the equation becomes:
I'll leave you to finish this.
Bob
]]>cos(A-B) + cos(A+B) = 2 cos(A) . cos(B)
A = 2x-5 and B = x+5
and a similar formula with a minus sign.
Bob
]]>Oops, that does not work. If tanAtanB = 1, then the denominator in the formula for tan(A+B) is 0.
Sorry, back to the drawing board …
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