Question

tana+ seca=3 then find sina​

Answer 1

Question= tana+ seca=3 then find

sina

Solution:

Given tanA+secA=3

so,sinA/cosA +1/cosA =3

sinA+1=3cosA

squaring on both sides,

1+(sinA)^2 +2sinA =9(cosA)^2

1+(sinA)^2 +2sinA =9(1-sinA^2)

SO, 10sinA^2+2sinA-8=0

5sinA^2 +sinA-4=0

SOLVING quadratic equation in sinA, we get sinA=4/5 OR sinA=-1

BUT WHEN sinA=-1 both tanA AND secA tends to infinity and will not give summation as 3 , so ,sinA has to be equal to be 4/5.