Apoorav J.

asked • 08/30/16

(secA-tanA)

(secA-tanA)2=cosecA-1/cosecA+1

Kenneth S.

Would you mind parenthesizing the right hand side of the proposed identity to make the order of operations airtight sure?  
 
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08/30/16

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Mark M. answered • 08/30/16

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(secA - tanA)2 = [1/cosA - sinA/cosA]2
 
                     = [(1 - sinA)/cosA]2
 
                     = (1 - sinA)2/cos2A
 
                     = (1 - sinA)2/[1 - sin2A]
 
                     = (1 - sinA)2/[(1 - sinA)(1 + sinA)]
 
                     = (1 - sinA)/(1+sinA)
 
                     = [1/sinA - sinA/sinA]/[1/sinA + sinA/sinA]
 
                     = (cscA - 1)/(cscA + 1)
 
 
 
                     
 
                    = sec2A - 2secAtanA + (sec2A - 1)
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