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3.Trigonometrical Ratios, Functions and Identities
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$4 \,\,sin5^o \,\,sin55^o \,\,sin65^o$ has the values equal to
A
$\frac{{\sqrt 3 + 1}}{{2\sqrt 2 }}$
B
$\frac{{\sqrt 3 - 1}}{{2\sqrt 2 }}$
C
$\frac{{\sqrt 3 - 1}}{{\sqrt 2 }}$
D
$\frac{{3\left( {\sqrt 3 - 1} \right)}}{{2\sqrt 2 }}$
Solution
$2[2sin\,5^o \,sin\,55^o] \,sin\,65^o$
$\Rightarrow$ $2[cos\,50^o – cos\,60^o]sin\,65^o$
$\Rightarrow$ $2cos\,50^o \,sin\,65^o – sin\,65^o$
$\Rightarrow$ $sin(115^o) + sin\,15^o – sin\,65^o = \frac{{\sqrt 3 – 1}}{{2\sqrt 2 }}$
Standard 11
Mathematics
