First slide

Trigonometric equations

Question

Which of the following gives the least value of $A$

Moderate

A

$\cos â¡ 2 A = \sin â¡ 3 A$
B

$\cos â¡ 3 A = \sin â¡ 7 A$
C

$\tan â¡ A = \cot â¡ 3 A$
D

$\cot â¡ A = \tan â¡ 2 A$

Solution

(a) $\cos â¡ 2 A = \sin â¡ 3 A = \cos â¡ (Ï / 2 â 3 A)$
$â 5 A = Ï / 2 = A = Ï / 10$
$(b) â 10 A = Ï / 2 â A = Ï / 20$
$(c) â A = Ï / 8, (d) â A = Ï / 6$
Least value of $A$ is $Ï / 20$ given by $(b) .$

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