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Solution 4.3:8b

From Förberedande kurs i matematik 1

Revision as of 10:53, 30 September 2008 by Ian (Talk | contribs)
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Because tanv=sinvcosv, the left-hand side can be written using cosv as the common denominator:


1cosvtanv=1cosvsinvcosv=cosv1-sinv


Now, we observe that if we multiply top and bottom by with 1+sinv, the denominator will contain the denominator of the right-hand side as a factor and, in addition, the numerator can be simplified to give 1sin2v =cos2v, using the conjugate rule:


cosv1-sinv=cosv1-sinv1+sinv1+sinv=1sin2vcosv1+sinv=cos2vcosv1+sinv


Eliminating cosv then gives the answer:


cos2vcosv1+sinv=cosv1+sinv