The two legs of a right triangle are `sin theta +sin ((3pi)/2-theta)` and `cos theta -cos( (3pi)/2-theta)` The length of its hypotenuse is hypotenuse is

Options

A. 1
B. 2
C. `sqrt(2)`
D. none of these

Answer

C

Explanation

`a =sin theta + sin((3pi)/(2)-theta)`
`=sin theta - cos theta`
`b = cos theta - cos((3pi)/(2)-theta)`
`= cos theta + sin theta`
`a^(2)+b^(2)=(sin theta - cos theta)^(2)+(sin theta +cos theta)^(2)=2`
`therefore` Hypotenuse `= c = sqrt(2)`