The most general solution of $$21+cosx+cosx2+cosx3+$$...∞$$=4$$ is $$2n$$π±πa, then $$a=$$

We have $$21+cosx+cosx2+cosx3+$$...∞$$=41+cosx+cosx2+$$.......∞ is in GP S∞$$=a1-r$$ ⇒$$211$$−$$cosx=22$$⇒$$11$$−$$cosx=2$$⇒$$cosx=12$$⇒$$cosx=$$±$$12$$⇒$$x=2n$$π±π$$3$$,n∈z ⇒$$a=3$$

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The most general solution of $2^{1 + |\cos x| + {|\cos x|}^{2} + {|\cos x|}^{3} + ... \infty} = 4 i s 2 n π \pm \frac{π}{a}, t h e n a =$

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Solution

$W e h a v e 2^{1 + |\cos x| + {|\cos x|}^{2} + {|\cos x|}^{3} + ... \infty} = 4$
$1 + |\cos x| + {|\cos x|}^{2} + . . . . . . . \infty i s i n G P S_{\infty} = \frac{a}{1 - r}$
$\begin{array}{l} \Rightarrow 2^{\frac{1}{1 - |\cos x|}} = 2^{2} \\ \Rightarrow \frac{1}{1 - |\cos x|} = 2 \\ \Rightarrow |\cos x| = \frac{1}{2} \\ \Rightarrow \cos x = \pm \frac{1}{2} \Rightarrow x = 2 n π \pm \frac{π}{3}, n \in z \end{array}$
$\Rightarrow a = 3$

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Trigonometric equations

Remember concepts with our Masterclasses.

The most general solution of 21+cosx+cosx2+cosx3+...∞=4 is 2nπ±πa, then a=

We have 21+cosx+cosx2+cosx3+...∞=41+cosx+cosx2+.......∞ is in GP S∞=a1-r ⇒211−cosx=22⇒11−cosx=2⇒cosx=12⇒cosx=±12⇒x=2nπ±π3,n∈z ⇒a=3

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The most general solution of $2^{1 + |\cos x| + {|\cos x|}^{2} + {|\cos x|}^{3} + ... \infty} = 4 i s 2 n π \pm \frac{π}{a}, t h e n a =$