Grade 12Trigonometry

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

chaman

12 Years agoGrade 12

2 Answers

Sunil Raikwar

12 Years ago

bsec@=c-atan@

squaring both sides

b²sec²@=c²+a²tan²@-2actan@

b²+b²tan²@=c²+a²tan²@-2actan@

(a²-b²)tan²@-2actan@+c²-b²=0

since tana & tanb are the roots of the equation

tana+tanb=2ac/a²-b², tanatanb=c²-b²/a²-b²

tan(a+b)=tana+tanb/1-tanatab=2ac/a²-b²

Thanks & Ragards

Sunil Raikwar

askIITians Faculty

Rinkoo Gupta

12 Years ago

bsec@=c-atan@squaring both sides
b2sec2@=c2+a2tan2@-2actan@
b2+b2tan2@=c2+a2tan2@-2actan@
(a2-b2)tan2@-2actan@+c2-b2=0
since tana & tanb are the roots of the equation
tana+tanb=2ac/a2-b2, tanatanb=c2-b2/a2-b2
tan(a+b)=tana+tanb/1-tanatab=2ac/a2-b2

Thanks & Regards

Rinkoo Gupta


AskIITians Faculty