Question
Simplify the following trigonometric expression:Â
15 cos 25° cosec 65° − 5 cot 80° cot 10°Solution
15 cos 25° cosec 65° − 5 cot 80° cot 10°
= 15 cos 25° cosec (90° − 25°) − 5 cot 80° cot (90° − 80°)
Using, cosec (90° − A) = sec A and cot (90° − A) = tan A
= 15 cos 25° sec 25° − 5 cot 80° tan 80°
Since, sec A is reciprocal of cos A and cot A is reciprocal of tan A.
= 15 − 5 = 10
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