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Find all the positive integral solutions of tan-¹x + cos-¹ [y/(1+y²)^1/2] = sin-¹ 3 /10 ^1/2

Find all the positive integral solutions of tan-¹x + cos-¹ [y/(1+y²)^1/2] = sin-¹ 3 /10 ^1/2

Grade:

1 Answers

Aditya Gupta
2080 Points
3 years ago
let tan^-1y=z
so  cos-¹ [y/(1+y²)^1/2]=pi/2 – z
rearranging, we get
tan-1x+cos-1(3/root10)=tan-1y
take tan both sides and apply formula of tan(A+B)=(tanA+tanB)/(1 – tanAtanB)
so that (3x+1)/(3 – x)=y
as both are positive integers, 3 – x>0
or x=1,2 corresponding to which y=2,7
hence, positve integral solutions are 
(x,y)=(1,2) or (2,7)

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