In `Delta ABC`, tan B `= sqrt(3)` , find the values of cosec B and cos B.

Explanation

Construct a right - angled triangle ABC in which `tanB=sqrt(3)=(sqrt(3))/(1)=("perpendicular")/("base")=(AC)/(AB)`
Let `AC=sqrt(3k)andAB=k`
From Pythagoras theorem
`BC^(2)=AB^(2)+AC^(2)`
`" " =(k)^(2)+(sqrt(3k))^(2)`
`" " BC^(2)=k^(2)+3k^(2)=4k^(2)`
`rArr " " BC=2k`
`:. " " "cosec" B=("hypotenuse")/("perpendicular")=(BC)/(AC)=(2k)/(sqrt(3k))=(2)/(sqrt(3))`
`and " " cos B=("base")/("hypotenuse")=(AB)/(BC)=(k)/(2k)=(1)/(2)`