If A = `4 sin theta + cos^(2) theta` , which of the following is not true ?(A) Maximum value of A is 5 .(B) Minimum value of A is `-4`(C) Maximum value of A occurs when `sin theta = 1//2`(D) Minimum value of A occurs when `sin theta = 1`.A. Maximum value of A is 5 .B. Minimum value of A is `-4`C. Maximum value of A occurs when `sin theta = 1//2`D. Minimum value of A occurs when `sin theta = 1`.

If A = `4 sin theta + cos^(2) theta` , which of the following is not t

1.	If A = `4 sin theta + cos^(2) theta` , which of the following is not true ?(A) Maximum value of A is 5 .(B) Minimum value of A is `-4`(C) Maximum value of A occurs when `sin theta = 1//2`(D) Minimum value of A occurs when `sin theta = 1`.A. Maximum value of A is 5 .B. Minimum value of A is `-4`C. Maximum value of A occurs when `sin theta = 1//2`D. Minimum value of A occurs when `sin theta = 1`.
Answer» (a) , ( c) , (d) `f(theta) = 4 sin theta cos^(2) theta = 4 sin theta + 1 - sin^(2) theta` `= 5 -(4-4sin theta + sin^(2) theta) = 5 - (sin theta -2)^(2)` Now maximum value of f`(theta)` occurs when `(sin theta -2)^(2)` is minimum . Minimum value of `(sin theta -2)^(2)` occurs when `sin theta =1` , then maximum value of `f(theta)" is " 5-(-1-2)^2=4`. Also minimum value of `f(theta)` occurs when `(sintheta-2)^2` is maximum. Mximum value of `(sintheta-2)^2` occurs when `sintheta=-1`, then minimum value of `f(theta)" is " 5-(-1-2)^2=-4`.