Which of the following is true ?

Options

A. `sin 765^(@)=-(1)/(sqrt(2))`
B. `cos(-(15pi)/(4))=-1`
C. `tan (13pi)/(3)=(1)/(sqrt(3))`
D. `cosec(-1410^(@))=2`

Answer

D

Explanation

`sin 765^(@)=sin(720^(@)+45^(@))=sin 45^(@)=(1)/(sqrt(2))`
`cot(-(15pi)/(4))=-cot((15pi)/(4))`
`=-cot(4pi-(pi)/(4))`
`=cot(pi)/(4)=1`
`tan.(13pi)/(3)=tan(4pi+(pi)/(3))=tan.(pi)/(3)=sqrt(3)`
`cosec(-1410^(@))=-cosec(1410^(@))`
`=-cosec(1410^(@)-30^(@))`
`=cosec(30^(@))=2`