Q. 173.5( 4 Votes )

If 3 sin x + 5 cos x = 5, then write the value of 5 sin x 3 cos x.

Answer :

3 sin x +5cos x = 5


3sin x = 5-5cos x


3sin x = 5(1-cos x)


Squaring both sides we get


9sin2x = 25(1-cos x)2


9sin2x = 25(1+cos2x-2cos x)


9sin2x+9cos2x = 25 + 25cos2x - 50cos x + 9cos2x


9(sin2x+ cos2x) = 25 +34cos2x-50cos x


34cos2x-50cos x+16=0


17cos2x-25cos x+8=0


17cos2x-17cos x-8cos x+8=0


17cos x(cos x-1)-8(cos x-1)=0



When cos x = 1


3sin x + 5cos x = 5


3sin x = 0


Sin x = 0


Substituting the value cos x = 1 and sin x = 0


5(0)-3(1) = 0-3


-3.



sin2x+ cos2x = 1


sin2x = 1- cos2x





5sin x – 3cos x




-3 and 3.


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