If the angle A of a triangle ABC is given by the equation 5 cos A + 3 = 0, then sin A and tan A are the roots of the equation

Options

A. `15x^(2)-8x-16=0`
B. `15x^(2)-8sqrt(2)x+16=0`
C. `15x^(2)-8x+16=0`
D. `15x^(2)+8x-16=0`

Answer

D

Explanation

`5 cos A + 3 = 0`
`rArr cos A = -3//5`
`rArr sin A = 4//5`
`rArr tan A = -4//3`
Now equation whose roots are 4/5 and -4/3 is
`(x-4//5)(x + 4//3)=0`
or `15x^(2)+8x - 16=0`