Question

If `2sin(x) + 5cos(y) + 7sin(z) = 14`, then what is the value of `7tan(x/2) + 4cos(y) - 6cos(z)` among the following option?

`A)4`
`B)-3`
`C)11`
`D)5`

Answer 1

11

Explanation:

Given that

`2sinx +5cosy+7sinz=14`

By inspection we see `x=pi/2,y=0and z=pi/2` satisfy the given equation.

Inserting these values in the expression we get

`7tan(x/2)+4cosy-6cosz`

`=7*tan(pi/4)+4*cos(0)-6*cos(pi/2)`

`=7*1+4*1-6*0=11`