Question

Given sec A = √85/6 write the value of cot a in the simplest fraction form

A.6/7
B.7/6
C.√85/7
D.7/√85

Answer 1

`\\ \sf\longmapsto sec^2A-1=tan^2A`

`\\ \sf\longmapsto tan^2A=((√85)^2)/(6^2)-1`

`\\ \sf\longmapsto tan^2A=(85)/(36)-1`

`\\ \sf\longmapsto tan^2A=(85-36)/(36)`

`\\ \sf\longmapsto tan^2A=(49)/(36)`

`\\ \sf\longmapsto tanA=(7)/(6)`

Now

`\\ \sf\longmapsto cotA=(1)/(tanA)=(6)/(7)`