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How do you use the double-angle identities to find cot(2x) if cos x= -15/17 and csc x is less than 0?

1 Answer

Jun 18, 2016

#161/240#

Explanation:

Given
#cosx =-15/17 and cscx<0->sinx<0#
#"both "cosx and sinx " being " <0 , color(blue)(" x is in 3rd quadrant")#

So #tanx>0#

#sinx =-sqrt(1-cos^2x)=-sqrt(1-(-15/17)^2)=-8/17#

#tanx = sinx/cosx=(-8/17)/(-15/17)=8/15#

Now

#cot2x=1/tan(2x)=(1-tan^2x)/(2tanx)=(1-(8/15)^2)/(2*8/15)#
#=161/15^2xx15/16=161/240#

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