SOLUTION: Verify the following identity. 1 / siny - 1 / siny + 1 = - 2sec^2 y

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Question 1206025: Verify the following identity.
1 / siny - 1 / siny + 1 = - 2sec^2 y
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
1 / siny - 1 / siny + 1 = - 2sec^2 y=> not quite readable, I assume you have

1+%2F+%28sin%28y%29+-+1%29-1+%2F+%28sin%28y%29+%2B+1%29+=+-2sec%5E2+%28y%29


manipulate left side
1+%2F+%28sin%28y%29+-+1%29-1+%2F+%28sin%28y%29+%2B+1%29+

=

=%28sin%28y%29+%2B+1++-sin%28y%29+%2B1%29+%2F+%28sin%5E2%28y%29+-+1%29

=2+%2F+%28sin%5E2%28y%29+-+1%29.......sin%5E2%28y%29-1=-cos%5E2%28y%29

=2+%2F+%28-cos%5E2%28y%29%29

=-2+%2F+cos%5E2%28y%29....use identity cos%5E2%28y%29=1%2Fsec%5E2+%28y%29

=-2+%2F+%281%2Fsec%5E2+%28y%29%29

=-2sec%5E2+%28y%29=> proven