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(Cos A/Sin A )+(1/Sin A)= 5 . Show that Cos A=12/13.

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$fraccos Asin A+frac1sin A=5\* fraccos A+1sinA=5Rightarrow (cos A+1)^2=(5sin A)^2\* ecause sin^2A+cos^2A=1\* cos^2A+1+2cos A=25(1-cos^2A)\* 26cos^2 A+2cos A-24=0\*26cos^2 A+26cos A-24cos A-24=0\* (cos A+1)(26cos A-24)=0\* cos A=-1;or;frac2426\* but;if;cos A=-1Rightarrow sin A=0,;for ;which;question;is;not;defined.;So,;cos A=frac2426=frac1213\* Hence,;proved$

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Deependra Verma

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