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Cos(x+y)=4/5 sin( x-y) =5/13 find tan2x where x, y lie bet 0,45degr

Cos(x+y)=4/5 sin( x-y) =5/13 find tan2x where x, y lie bet 0,45degr

Grade:11

2 Answers

Arun
25758 Points
5 years ago
now sin(x+y)= 3/5
and sin(x-y) 5/13 is given hence sin(x+y) +sin(x-y)= 2sinx cosy= 64/65
cos (x-y)= 12/13 hence cos(x+y)+ cos(x-y)= 2cosx cosy= 112/65
now tanx = 64/112
now you can simply put the formula of tan2x
User
7 Points
5 years ago
x+y = cos^-1(4/5)x-y = sin^-1(5/13)Now convert them in term of tan^-1 by making triangle after converting to tan^-1 we get x+y = tan^-1 (3/4).…...........(1) x-y = tan^-1 (5/12)..............(2) Now add both of them2x = tan^-1(3/4) + tan^-1(5/12)taking tan on both sideand also apply (tan^-1a + tan-^1b) formulatan(2x) = tan[tan^-1{(3/4 + 5/12)/(1-3/4×5/12)}]tan(2x) = 56/33

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