Question

If sec x =2then find sin x, cos x ,tan x, cosec x, sec x,cot x, cot x+cosec x ?

Answer 1

It is given that, `sec x =2`

we know, `color(red)(cosx = 1/secx`
`=> cosx=1/2`

by the identity, `color(red)(sin^2x + cos^2x = 1`

`sin^2x = 1 -(1/2)^2`
`=>sinx = sqrt3/2`

we know, `color(red)(sinx= 1/cscx`
`=> cscx=2/sqrt3`

by definition, `color(red)(tanx = sinx/cosx`
`=> tanx = sqrt3/2 xx 2 = sqrt3`

we know, `color(red)(cotx= 1/tanx`
`=> cotx=1/sqrt3`

now, `cotx +cscx= 1/sqrt3 + 2/sqrt3 = 3/sqrt3 = sqrt3`

Answer 2

Please see explanation below.

Explanation:

If ,`0< x < pi/2`
`secx=2rArrcosx=1/secxrArrcosx=1/2`
`sinx=sqrt(1-cos^2x)=sqrt(1-1/4)=sqrt(3/4)=sqrt3/2`
`rArrcscx=1/sinx=1/(sqrt3/2)=2/sqrt3`
`tanx=sinx/cosx=((sqrt3)/(2))/(1/2)=sqrt3`
`rArrcotx=1/tanx=1/sqrt3`
Also,`cotx+cscx=1/sqrt3+2/sqrt3=(1+2)/sqrt3=3/sqrt3=sqrt3.`