Question
Thu August 16, 2012 By:

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

Expert Reply
Thu August 16, 2012

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

Related Questions
Ask the Expert