First slide

Compound angles

Question

$Let x = \sin 1^{0} then the value of \frac{1}{\cos 0^{0} \cos 1^{0}} + \frac{1}{\cos 1^{0} \cos 2^{0}} + \dots \dots \dots \dots + \frac{1}{\cos 44^{0} \cos 45 °} =$

Moderate

A

$\frac{\sqrt{2}}{x}$
B

$\frac{x}{\sqrt{2}}$
C

$\frac{1}{x}$
D

$x$

Solution

We have
$\begin{array}{l} \frac{1}{\sin 1^{0}} [\frac{\sin 1^{0}}{\cos 1^{0}} + \frac{\sin (2^{0} - 1^{0})}{\cos 1^{0} \cos 2^{0}} + \dots \dots \dots + \frac{\sin (45 ° - 44^{0})}{\cos 44^{0} \cos 41^{0}}] \\ = \frac{1}{\sin 1^{0}} [\tan 1^{0} + \tan 2^{0} - \tan 1^{0} + \tan 3^{0} - \tan 2^{0} + \dots \dots \dots \tan 45 ° - \tan 44^{0}] \\ = \frac{1}{x} \end{array}$

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