Question 101

If cot A + cosec A = 3 and A is an acute angle, then the value of cos A is :

Solution

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cosec A + cot A =3
cosec²A-cot²A=1;
cosec A-cot A = 1/(cosec A+cot A)
So cosec A - cot A =1/3
2 cosec A=10/3 or cosec A=5/3.
Hence sin A=3/5
cos²a=1-sin²a
So ,cos²a= 1 - (9/25) = 16/25
cos A=4/5.
Option A is the correct answer.

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