IF 5sinA+3cosA=4 ,then find the value of 3sinA-5cosA .

Asked by  | 16th Aug, 2012, 10:08: AM

Expert Answer:

We would request you to please cross check the question you posted. However, you can proceed in the following way in such types of questions:

 

(a sin A + b cos A )^2 + (b sin A - a cos A) ^2

= a^2 sin ^2 A + b^2 cos^2 A + 2ab sin A cos A + b^2 sin ^2 A + a^2 cos ^2 A - 2ab cos A sin A
= a^2 + b^2

 

Therefore,

(5sinA + 3cosA)^2 + (3sinA - 5 cosA)^2 = 5^2 + 3^2

16 + (3sinA - 5 cosA)^2 = 25 + 9

(3sinA - 5 cosA)^2 = 18

3sinA - 5 cosA = 3 sqrt 2

Answered by  | 16th Aug, 2012, 03:30: PM

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