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5 sin x+4cos x=3,4sinx-5cos x= |
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Answer» 5sinx+4cosx=3Squaring both sides25sin 2 x+16cos 2 x+2∗5∗4sinxcosx=9⇒9sin 2 x+7+40sinxcosx=0⇒9sin 2 x+7=−40sinxcosxNow, 4sinx−5cosx= (4sinx−5cosx) 2 = 16sin 2 x+25cos 2 x−40sinxcosx = 16sin 2 x+25cos 2 x+9sin 2 x+7 = 25sin 2 x+25cos 2 x+7 = 25+7 = 32 =4 ROOT 2 |
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