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How do you simplify #cos[2(tan^(-1)(-4/3))]#?

1 Answer

A. S. Adikesavan

Aug 9, 2016

#-7/25#

Explanation:

Let #a = tan^(-1)(-4/3) in Q4#.

Then, #tan a = -4/3 < -1 = tan -(pi/4)#. So, # 2a < -pi/2 and in Q3#.

And so, cos a = 3/5 and cos 2a < 0. .

The given expression is

#cos 2a =2 cos^2a-1= 2(3/5)^2-1=-7/25#.

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