if a and b are two values of x lying between 0 and 360 which satisfy equation 6cosx+ 8sinx=9 then what will be the value of sin(a+b)
Answers
Answered by
2
6cosx + 8sinx = 9
10 { 6/10 × cosx + 8/10 × sinx } = 9
10{ cosß × cosx + sinß × sinx } = 9
cos{ x - ß } = 9/10
so,
x - ß = 2nπ ± cos^-1(9/10 )
x = ß + 2nπ ±cos^-1(9/10)
where n is integer , ß = tan^-(4/3)
two values between 0 to 2π are
ß + cos^-(9/10) , ß -cos^-1(9/10)
so,
sin( a+ b) = sin{ ß + cos^-1(9/10)+ ß -cos^-1(9/10) }
= sin2ß
=2tanß/( 1+tan²ß)
=2×4/3/( 1+4²/3²)
=8/3 /( 9+16)/9
= 24/25
10 { 6/10 × cosx + 8/10 × sinx } = 9
10{ cosß × cosx + sinß × sinx } = 9
cos{ x - ß } = 9/10
so,
x - ß = 2nπ ± cos^-1(9/10 )
x = ß + 2nπ ±cos^-1(9/10)
where n is integer , ß = tan^-(4/3)
two values between 0 to 2π are
ß + cos^-(9/10) , ß -cos^-1(9/10)
so,
sin( a+ b) = sin{ ß + cos^-1(9/10)+ ß -cos^-1(9/10) }
= sin2ß
=2tanß/( 1+tan²ß)
=2×4/3/( 1+4²/3²)
=8/3 /( 9+16)/9
= 24/25
Similar questions