Ac A.
asked • 08/25/19Simplify expression
| sin(5x)-sin(3x)/sin(5x)+sin(3x)=tan(x)/tan(4x) |
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1 Expert Answer
Steve M. answered • 08/25/19
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(214)
Algebra, Trig, Calculus -- Learn to Love it as I Do
Recalling your sum-to-product formulas,
sin5x - sin3x = 2 cos4x sinx
sin5x + sin3x = 2 sin4x cosx
Now divide, and you have
(2 cos4x sinx)/(2 sin4x cosx) = cos4x/sin4x * sinx/cosx = cot4x * tanx = tanx/tan4x
Ac A.
Can I apply sum and difference formula?
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08/25/19
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Stephen C.
the apparent left side intention is: (sin(5x) - sin(3x)) / (sin(5x) + sin(3x)). At least, the equation is then true at least for x = 30 degrees.08/25/19