Question 138

Evaluate : 3 cos 80° cosec 10° + 2 cos 59° cosec 31°

Solution

We need to find find value of : 3 cos 80° cosec 10° + 2 cos 59° cosec 31°

3 cos 80 cosec (90-80) + 2 cos 59 cosec (90 - 59)

3 cos 80 sec 80 + 2 cos 59 sec 59

as, cos 80 sec 80 = cos 59 sec 59 = 1, then

3 cos 80 sec 80 + 2 cos 59 sec 59 = 3 + 2 = 5

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