IF ` tan alpha = ( sin alpha - cos alpha )/( sin alpha + cos alpha)` , then ` sin alpha + cos alpha` is

Options

A. less than `pi//6`
B. greater than `pi//6`
C. less than `pi//3`
D. greater than `pi//3`

Answer

C

Explanation

In the graph of `y=sinx`.Let
`A-=(alpha,sinalpha),B=(pi/6,sin.pi/6)`

Clearly, shope of OA gt slope of OB,so
`sinalpha/alphagt(sinpi//6)/(pi//6)=3/pirArralpha/sinalphaltpi/3`.