Question

If cos(x) = (1/4), where x lies in quadrant 4, how do you find tan(x - pi/4)?

Answer 1

The reqd. value`=(sqrt15+1)/(sqrt15-1)`.

Explanation:

We have, `tan(x-pi/4)=(tanx-tan(pi/4))/(1+tanxtan(pi/4))`

`=(tanx-1)/(1+tanx)=((sinx-cosx)/(sinx+cosx))`

So, we need `sin x` to find the reqd. value.

`cos x=1/4, x in Q_(IV) rArr sinx=-sqrt(1-cos^2x)=-sqrt15/4`.

Hence, the reqd. value`=(-sqrt15/4-1/4)/(-sqrt15/4+1/4)=(sqrt15+1)/(sqrt15-1)`.