if a and b are the solutions of the equation atan@+bsec@=c then show that
tan(a+b)=2ac/(a^2-c^2)

Question

if a and b are the solutions of the equation atan@+bsec@=c then show that tan(a+b)=2ac/(a^2-c^2)

Sunil Raikwar · Answer

bsec@=c-atan@ squaring both sides b 2 sec 2 @=c 2 +a 2 tan 2 @-2actan@ b 2 +b 2 tan 2 @=c 2 +a 2 tan 2 @-2actan@ (a 2 -b 2 )tan 2 @-2actan@+c 2 -b 2 =0 since tana & tanb are the roots of the equation tana+tanb=2ac/a 2 -b 2 , tanatanb=c 2 -b 2 /a 2 -b 2 tan(a+b)=tana+tanb/1-tanatab=2ac/a 2 -b 2 Thanks & Ragards Sunil Raikwar askIITians Faculty

Rinkoo Gupta · Answer

bsec@=c-atan@ squaring both sides b 2 sec 2 @=c 2 +a 2 tan 2 @-2actan@ b 2 +b 2 tan 2 @=c 2 +a 2 tan 2 @-2actan@ (a 2 -b 2 )tan 2 @-2actan@+c 2 -b 2 =0 since tana & tanb are the roots of the equation tana+tanb=2ac/a 2 -b 2 , tanatanb=c 2 -b 2 /a 2 -b 2 tan(a+b)=tana+tanb/1-tanatab=2ac/a 2 -b 2 Thanks & Regards Rinkoo Gupta AskIITians Faculty

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if a and b are the solutions of the equation atan@+bsec@=c then show that tan(a+b)=2ac/(a^2-c^2)

if a and b are the solutions of the equation atan@+bsec@=c then show that
tan(a+b)=2ac/(a^2-c^2)

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