How do you find the value of #tan(theta/2)# given #costheta=-15/17# and #180<theta<270#?

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Answer 1 · 2018-04-25T06:40:32

# -4#.

We will use the Identity :

# tan^2(theta/2)=(1-costheta)/(1+costheta)#.

#:. tan^2(theta/2)={1-(-15/17)}/{1+(-15/17)}#,

#=(17+15)/(17-15)#,

#=32/2#,

#=16#.

#:. tan(theta/2)=+-4#.

But, we know that, #180 lt theta lt 270#.

#:. 180/2 lt theta/2 lt 270/2, or, #

# 90 lt theta/2 lt 135#.

This means that #theta/2# is in the #2^(nd)# Quadrant, where,

#tan# is #-ve#.

#:. tan(theta/2)=-4#.