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3.Trigonometrical Ratios, Functions and Identities
normal
$x$ ............ કિમત માટે $x = 1 - x + x^2 - x^3 + x^4 - x^5 + ......... \infty$ થાય
A
$2\, cos36^°$
B
$2 \,cos144^°$
C
$2\, sin18^°$
D
એક પણ નહીં
Solution
$x = \frac{1}{{1 + x}}$ $\Rightarrow$ $x^2 + x – 1 = 0$
$x = \frac{{ – 1 + \sqrt 5 }}{2}$ or $\frac{{ – 1 – \sqrt 5 }}{2}$ (rejected, think ! )
hence $x = \left( {\frac{{\sqrt 5 – 1}}{4}} \right)\,\cdot\,2 = 2 \, sin18^°$
Standard 11
Mathematics
