First slide

Trigonometric transformations

Question

The value of cosec10° + cosec 50° - cosec 70° is

Easy

A

5
B

2
C

1
D

6

Solution

$\frac{1}{\sin 10 °} + \frac{1}{\sin 50 °} - \frac{1}{\sin 70 °}$
$= \frac{1}{\cos 80 °} + \frac{1}{\cos 40 °} - \frac{1}{\cos 20 °}$

$\frac{\cos 40 ° \cos 20 ° + \cos 80 ° \cos 20 ° - \cos 40 ° \cos 80 °}{\cos 20 ° . \cos 40 ° . \cos 80 °}$

$= 8 [\cos 20 ° (\cos 40 ° + \cos 80 °) - \cos 40 ° \cos 80 °]$

$= 8 [2 \cos 20 ° \cos 60 ° \cos 20 ° - \cos 40 ° \cos 80 °]$

$= 4 [2 \cos^{2} 20 ° - 2 \cos 40 ° \cos 80 °]$

$= 4 [1 + \cos 40 ° - (\cos 120 ° + \cos 40 °)]$

$= 4. \frac{3}{2} = 6$

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