The maximum value of cos2(π3−x)−cos2(π3+x) is

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Question

The maximum value of

c o s^{2} (\frac{π}{3} - x) - c o s^{2} (\frac{π}{3} + x)

is

Options:

A . - √32

B . 12

C . √32

D . 32

Answer: Option C
:
C

c o s^{2} (\frac{π}{3} - x)

-

c o s^{2} (\frac{π}{3} + x)

=

{c o s (\frac{π}{3} - x) + c o s (\frac{π}{3} + x)}

{c o s (\frac{π}{3} - x) - c o s (\frac{π}{3} + x)}

=

{2 c o s \frac{π}{3} c o s x}

{2 s i n \frac{π}{3} s i n x}

= sin

\frac{2 π}{3}

sin 2x =

\frac{\sqrt{3}}{2}

sin 2x
Its maximum value is

\frac{\sqrt{3}}{2}

, {- 1

\leq

sin 2x

\leq

1}.

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