5 sin x+4cos x=3,4sinx-5cos x=

1.	5 sin x+4cos x=3,4sinx-5cos x=
Answer» <html><body><p>5sinx+4cosx=3Squaring both sides25sin <a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a> 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 = <a href="https://interviewquestions.tuteehub.com/tag/32-307188" style="font-weight:bold;" target="_blank" title="Click to know more about 32">32</a> =<a href="https://interviewquestions.tuteehub.com/tag/4-311707" style="font-weight:bold;" target="_blank" title="Click to know more about 4">4</a> <a href="https://interviewquestions.tuteehub.com/tag/root-1190914" style="font-weight:bold;" target="_blank" title="Click to know more about ROOT">ROOT</a> 2</p></body></html>

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