SOLUTION: Verify the identity. (1/cosx+1) + (1/cosx-1) = -2cscx cot x

Algebra ->  Trigonometry-basics -> SOLUTION: Verify the identity. (1/cosx+1) + (1/cosx-1) = -2cscx cot x      Log On


   

Question 1076620: Verify the identity.
(1/cosx+1) + (1/cosx-1) = -2cscx cot x
Found 2 solutions by stanbon, MathTherapy:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Verify the identity.
(1/cosx+1) + (1/cosx-1) = -2cscx cot x
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Multiply thru by cos^2(x)-1 to get:
Note:: cos^2(x)-1 = -sin^2(x)
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cos(x)-1 + cos(x)+1 = (-sin^2(x))(-2csc(x)cot(x))
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2cos(x) = 2*sin(x)cos(x)
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Ans:: Not an identity
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Cheers,
Stan H.
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Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!

Verify the identity.
(1/cosx+1) + (1/cosx-1) = -2cscx cot x
1%2F%28cos+%28x%29+%2B+1%29+%2B+1%2F%28cos+%28x%29+-+1%29+=+-+2+csc+%28x%29+cot+%28x%29

Left side: %28cos+%28x%29+-+1+%2B+cos+%28x%29+%2B+1%29%2F%28cos+%28x%29+%2B+1%29%28cos+%28x%29+-+1%29 ------ Multiplying by LCD, (x + 1)(x - 1)

            %282+cos+%28x%29%29%2F%28cos%5E2+%28x%29+-+1%29

            %282+cos+%28x%29%29%2F%281+-+sin%5E2+%28x%29+-+1%29 ------- Substituting matrix%281%2C3%2C+1+-+sin%5E2+%28x%29%2C+for%2C+cos%5E2+%28x%29%29

            %282+cos+%28x%29%29%2F%28-+sin%5E2+%28x%29%29 =======> %28-+2+%2A+cos+%28x%29%29%2Fsin%5E2+%28x%29 =======> -+2+%2A+%28cos+%28x%29%2Fsin+%28x%29%29+%2A+%281%2Fsin+%28x%29%29 =======> highlight_green%28-+2+%2A+cot+%28x%29+%2A+csc+%28x%29%29 (Same as RIGHT side so this has been proven)