- Home
- Standard 11
- Mathematics
3.Trigonometrical Ratios, Functions and Identities
hard
The value of ${\cos ^2}\,{10^o}\,\, - \,\cos \,\,{10^o}\,\cos \,\,{50^o}\, + \,{\cos ^2}\,{50^o}$ is
A
$\frac{3}{2}\,(1\, + \,\cos \,{20^o})$
B
$\frac {3}{4}$
C
$\frac {3}{2}$
D
$\frac{3}{4}\,\, + \,\,\cos \,{20^o}$
(JEE MAIN-2019)
Solution
$\frac{1}{2}\,(2\,{\cos ^2}{10^o}\, – \,2\cos \,{10^o}\,\cos \,{50^o} + \,2\,{\cos ^2}{50^o})$
$ \Rightarrow \frac{1}{2}\,(1 + \,\cos \,{20^o} – (\cos \,{60^o} + \cos \,{40^o})\, + 1 + \,\,\cos {100^o})$
$ \Rightarrow \frac{1}{2}\,\left( {\frac{3}{2} + \,\cos \,{{20}^o} + 2\sin \,{{70}^o}\sin \,( – {{30}^o})} \right)$
$ \Rightarrow \frac{1}{2}\,\left( {\frac{3}{2} + \,\cos \,{{20}^o} – \sin \,{{70}^o}} \right)$
$ \Rightarrow \frac{3}{4}$
Standard 11
Mathematics
