First slide

Trigonometric Identities

Question

$If x∈ (\frac{3 π}{4}, π), t h e n t h e v a l u e o f \frac{|c o s x| + |c o s 2 x|}{(2 c o s x + 1) (c o s x - 1)} i s$

Easy

A

1
B

0
C

-1
D

2

Solution

$\frac{|c o s x| + |c o s 2 x|}{(2 c o s x + 1) (c o s x - 1)} = \frac{- \cos x + \cos 2 x}{(2 \cos x + 1) (\cos x - 1)} (|\cos x| = - \cos x w h e n x \in (\frac{3 π}{4}, π) and |\cos 2 x| = \cos 2 x w h e n 2 x \in (\frac{3 π}{2}, 2 π)) \Rightarrow g i v e n q u e s t i o n = \frac{- \cos x + 2 \cos^{2} x - 1}{(2 c o s x + 1) (c o s x - 1)}$
$= \frac{(2 \cos x + 1) (\cos x - 1)}{(2 \cos x + 1) (\cos x - 1)} = 1$

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