What is the value of `(sintheta+costheta-tantheta)/(sectheta+"cosec"-cot theta)`, when `theta=(3pi)/(4)`?

Options

A. 0
B. 1
C. `-1`
D. None of these

Answer

B

Explanation

Consider
`(sintheta+costheta-tantheta)/(sectheta+cosectheta-cot theta)`
Now , put value of `theta=(3pi)/(4)`, we get
`("sin"(3pi)/(4)+"cos"(3pi)/(4)-"tan"(3pi)/(4))/("sec"(3pi)/(4)+cosec(3pi)/(4)-"cot"(3pi)/(4))`
`=("sin"(pi)/(4)-"cos"(pi)/(4)+"tan"(pi)/(4))/(-(1)/("cos"(pi)/(4))+(1)/("sin"(pi)/(4))+(1)/("tan"(pi)/(4)))=((1)/(sqrt(2))-(1)/(sqrt(2))+1)/(-sqrt(2)+sqrt(2)+1)=1`