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a sin A +b cos A=c then prove a cosA -c sin A =under root a sq. + b sq.- c

Asked by pooja anand 4th August 2012, 6:13 PM
Answered by Expert
Answer:
Given, a sin A +b cos A = c
Squaring both sides, we get,
a2 sin2 A +b2 cos2 A + 2ab sinA cosA = c2
a2 (1- cos2 A) +b2 (1- sin2 A) + 2ab sinA cosA = c2
a2 - a2 cos2 A +b2 - b2 sin2 A + 2ab sinA cosA = c2
a2 +b2 - (a2 cos2 A + b2 sin2 A - 2ab sinA cosA) = c2
a2 +b2 - (a cos A - b sinA)2 = c2
(a cos A - b sinA)2 = a2 +b2 - c2
a cos A - b sinA = sqrt (a2 +b2 - c2)
Answered by Expert 4th August 2012, 11:00 PM
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