( cosec A - sin A )( sec A - cos A )= 1/tanA + cotA
Asked by | 13th Aug, 2012, 01:13: PM
Expert Answer:
(cosecA-sinA)(secA-cosA)
=(cosecAsecA-cosecAcosA-sinAsecA+sinAcosA) by multiplying the binomials.
=1/(sinAcosA)-(cosA/sinA)-
(sinA/cosA)+sinAcosA by rewriting in terms of sine and cosine
=[1-cos2A-sin2A+sin2Acos2A]
--------------------------------------
getting a common denominator.
SinAcosA
=sinAcosA ...by simplifying
=1/[1/sinAcosA]
=1/[(sin2A+cos2A)/sinAcosA]
=1/[sinA/cosA +cosA/sinA]
=1/(tanA+cotA)
=(cosecAsecA-cosecAcosA-sinAsecA+sinAcosA) by multiplying the binomials.
=1/(sinAcosA)-(cosA/sinA)-
(sinA/cosA)+sinAcosA by rewriting in terms of sine and cosine
=[1-cos2A-sin2A+sin2Acos2A]
-------------------------------------- getting a common denominator.
SinAcosA
=sinAcosA ...by simplifying
=1/[1/sinAcosA]
=1/[(sin2A+cos2A)/sinAcosA]
=1/[sinA/cosA +cosA/sinA]
=1/(tanA+cotA)
Answered by | 13th Aug, 2012, 02:35: PM
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