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VMariaS [17]
4 years ago
6

Given tan of theta = -2 and pi/2; find cos(2theta)

Mathematics
2 answers:
worty [1.4K]4 years ago
8 0

Answer:

[D]  cos2θ = - 3/5

Nata [24]4 years ago
5 0

Given tan of theta = -2 and pi/2; find cos(2theta)
The identity of cos (2 theta)= cos(2\theta )=\frac{1-tan^2\theta }{1+tan^2\theta }
Given tan of theta = -2 and pi/2.
So, let's plug in tan theta= -2
cos(2\theta)= \frac{1-(-2)^2}{1+(-2)^2}
=\frac{1-4}{1+4} (Squaring)
=\frac{-3}{5} (simplifying)
So, cos ( 2 theta) = -3/5.
Now we can plug in tan theta = π/2
cos(2\theta)= \frac{1-(π/2)^2}{1+(π/2)^2}
= \frac{1-pi^2/4}{1+pi^2/4} (Squaring)
=\frac{4-pi^2}{4+pi^2} Simplifying
So, cos ( 2 theta)= -3/5 and (4-pi^2)/(4+pi^2)

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