1.

Find the general values of x and y satisfying the equations `5sinx cosy=1`; `4tanx =tany`

Answer» We have
`5 sin x cos y=1 and 4 tan x= tan y`
or `5 sin x cos y=1 and 4 sin x cos y= sin y cos x`
or `sin x cos y =1/5 and cos x sin y =4/5`
`rArr sin x cos y + cos x sin y=1`
and `sin x cos y - cos x sin y =- 3/5`
`rArr sin (x+y)="sin"pi/2 and sin (x-y)= sin {sin^(-1)(-3/5)}`
`rArr x+y=n pi +(-1)^(n) pi/2 n in Z`
and `x-y=m pi + (-1)^(m) sin^(-1) (-3/5), m in Z`
`rArr x=(m+n) pi/2+(-1)^(n) pi/4+(-1)^(m) 1/2 sin^(-1) (-3/5) , m, n in Z`
and `y=(n-m) pi/2+(-1)^(n) pi/4 + (-1)^(m+1)1/2 sin^(-1) (-3/5), m, n in Z`


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