Question 77437: (1) The expression (1+cosA)/(1-cosA)- (secA-1)/(1+secA)-4cot^2A, wherever definrd simplifies to:
(a) 1/1+secA (b) 4/1+secA (c) 4/1+sinA (d) 1/1+tanA Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! (1) The expression (1+cosA)/(1-cosA)- (secA-1)/(1+secA)-4cot^2A, wherever definrd simplifies to:
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The 2nd term simplifies as follows:
(1/cos - 1)/(1+ 1/cos)
=(1-cos)/cos / (1+cos)/cos
=(1-cos)/(1+cos)
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Putting that back into the problem you now have:
[(1+cos)/(1-cos)]-[(1-cos)/(1+cos)] - 4cot^2
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Combine terms 1 and 2 with an lcd of (1-cos)(1+cos) =sin^2 to get:
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[(1+cos)^2-(1-cos)^2]/sin^2 -4cot^2
Simplify the numerator to get:
=4cos^2/sin2 - 4cot^2
=0
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Cheers,
Stan H.
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