First slide

Multiple and sub- multiple Angles

Question

The greatest value of $\cos Î¸$ for which $\cos 5 Î¸ = 0$ is

Moderate

A

0
B

$(1 + \sqrt{5}) / 4$
C

$\sqrt{\frac{5 + \sqrt{5}}{8}}$
D

$\sqrt{\frac{\sqrt{5} + 1}{4}}$

Solution

$\cos â¡ 5 Î¸ = 0 â 5 Î¸ = 2 n Ï Â\pm Ï / 2$
As $\cos Î¸$ decreases in $[0, Ï / 2]$ , it is greatest when $Î¸$ is least,
i .e. $Î¸ = Ï / 10 = 18^{â}$ and $\cos â¡ Î¸ = \cos â¡ 18^{â} = \sqrt{\frac{5 + \sqrt{5}}{8}}$

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