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

1 Answer

Aug 27, 2016

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)#.

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