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3.Trigonometrical Ratios, Functions and Identities
normal
The value of $\left( {1 + \cos \frac{\pi }{9}} \right)\left( {1 + \cos \frac{{3\pi }}{9}} \right)\left( {1 + \cos \frac{{5\pi }}{9}} \right)\left( {1 + \cos \frac{{7\pi }}{9}} \right)$ is
A
$\frac{9}{{16}}\,$
B
$\frac{10}{{16}}\,$
C
$\frac{12}{{16}}\,$
D
$\frac{5}{{16}}\,$
Solution
$E = \frac{3}{{2}} (1 + cos20^o) (1 + cos100^o) (1 + cos140^o) $
$= \frac{3}{{2}} 2\, cos^210^o . 2cos^250^o . 2\, cos^270^o$
$= 12(cos10^o\, cos50^o\, cos70^o)^2 = 12 × \frac{3}{{64}}\, = \frac{9}{{16}}\,$
Standard 11
Mathematics
