SOLUTION: sin(x+y)/cos(x+y) - sinx/cosx how to simplify even sin(x+y) making cos alpha + beta formula

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Question 1058012: sin(x+y)/cos(x+y) - sinx/cosx
how to simplify even sin(x+y) making cos alpha + beta formula
Answer by solve_for_x(190) About Me  (Show Source):
You can put this solution on YOUR website!
Multiply the first term by cos(x)/cos(x), and the second term by cos(x + y)/cos(x + y), which gives:





Expanding sin(x + y) and cos(x + y) then gives:





+%28cos%5E2%28x%29sin%28y%29+%2B+sin%5E2%28x%29sin%28y%29%29+%2F+cos%28x%29cos%28x+%2B+y%29+

+%28%28cos%5E2%28x%29+%2B+sin%5E2%28x%29%29sin%28y%29%29+%2F+cos%28x%29cos%28x+%2B+y%29+

+%28%281%29sin%28y%29%29+%2F+cos%28x%29cos%28x+%2B+y%29+

+sin%28y%29+%2F+cos%28x%29cos%28x+%2B+y%29+

If you want to go a step farther, the above expression is equivalent to:

+sec%28x%29sin%28y%29+%2F+cos%28x+%2B+y%29+