If f ( θ ) = 1 − sin θ − 1 cos θ 1 sin θ 1 − cos θ 1 and A and B are respectively the maximum and the minimum values of f ( θ ) , then ( A , B ) is equal to:

Question

If f ( θ ) = ​ 1 − sin θ − 1 ​ cos θ 1 sin θ ​ 1 − cos θ 1 ​ ​ and A and B are respectively the maximum and the minimum values of f ( θ ) , then ( A , B ) is equal to:

TestHub · Accepted Answer

​ Let f ( θ ) = ​ 1 − sin θ − 1 ​ cos θ 1 sin θ ​ 1 − cos θ 1 ​ ​ = ( 1 + sin θ cos θ ) − cos θ ( − sin θ − cos θ ) + 1 ( − sin 2 θ + 1 ) = 1 + sin θ cos θ + sin θ cos θ + = 2 + 2 sin θ cos θ + cos 2 θ = 2 + sin 2 θ + cos 2 θ ​ Now, maximum value of (1) is 2 + 1 2 + 1 2 ​ = 2 + 2 ​ and minimum value of (1) is 2 − 1 2 + 1 2 ​ = 2 − 2 ​ .

Mathematics - Determinant Question with Solution | TestHub

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