( 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)

Answered by  | 13th Aug, 2012, 02:35: PM

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