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Trigonometrical Equations
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If$\cos 6\theta + \cos 4\theta + \cos 2\theta + 1 = 0$, where $0 < \theta < {180^o}$, then $\theta =$
A
${30^o},{45^o}$
B
${45^o},{90^o}$
C
${135^o},{150^o}$
D
${30^o},{45^o},{90^o},{135^o},{150^o}$
Solution
(d) $\cos 6\theta + \cos 4\theta + \cos 2\theta + 1 = 0$
$ \Rightarrow $$2{\cos ^2}3\theta + 2\cos 3\theta \,.\,\cos \theta = 0$
$ \Rightarrow $ $4\cos 3\theta \cos 2\theta \cos \theta = 0$
$ \Rightarrow $ $3\theta = (2n + 1)\frac{\pi }{2};\,\,2\theta = (2n + 1)\frac{\pi }{2}{\rm{\, and\,\, }}\theta = (2n + 1)\frac{\pi }{2}$
$ \Rightarrow $ $\theta = {30^o},\,{90^o},\,{150^o},\,{45^o},\,{135^o}$.
Standard 11
Mathematics
