The solution set of the equation
`("sin" 13^(@))^("cot" 3x+ "cot"x) = "sin"^(2) (4pi-x)-"cos" (3pi-x) "cos" (2 pi +x)` is given by

Options

A. `x = (n pi)/(4), n ne 4 lambda, lambda in Z`
B. `x = (n pi)/(2), n ne 2 lambda, lambda in Z`
C. `x = (n pi)/(3), n in 3 lambda`
D. none of these

Answer

A

Explanation

The given equation is defined, if `x ne n pi, n in Z`.
Now,
`("sin" 13^(@))^("cot" 3x + "cot"x)`
` = "sin"^(2) (4pi-x)-"cos" (3pi-x) "cos" (2pi +x)`
`rArr ("sin" 13^(@))^("cot"3x + "cot"x) = "sin"^(2)x + "cos"^(2)x = 1 = ("sin" 13^(@))^(0)`
`rArr "cot" 3x + "cot"x =0`
`rArr "sin" 4x = 0`
`rArr 4x = n pi, n in Z`
`rArr x - (npi)/(4), n in Z`
Hence, `x = (npi)/(4), n ne 4 lambda, lambda in Z` is the solution of the given equation.