Question
Simplify the following trigonometric expression:
8 cos 40° cosec 50° − 2 cot 30° cot 60°Solution
8 cos 40° cosec 50° − 2 cot 30° cot 60°
= 8 cos 40° cosec (90° − 40°) − 2 cot 30° cot (90° − 30°)
Using, cosec (90° − A) = sec A and cot (90° − A) = tan A
= 8 cos 40° sec 40° − 2 cot 30° tan 30°
Since, sec A is reciprocal of cos A and cot A is reciprocal of tan A.
= 8 − 2 = 6
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