Match the following. List-I List-II (a) The maximum value of cos ( 2 A + θ ) + cos ( 2 B + θ ) ( θ ∈ R and A , B are constants) (p) 2 sin ( A + B ) (b) Maximum value of ( A , B ∈ ( 0 , 2 π ) , A + B

Question

Match the following. List-I List-II (a) The maximum value of cos ( 2 A + θ ) + cos ( 2 B + θ ) ( θ ∈ R and A , B are constants) (p) 2 sin ( A + B ) (b) Maximum value of ( A , B ∈ ( 0 , 2 π ​ ) , A + B cos 2 A + cos 2 B is constant) (q) 2 sec ( A + B ) (c) Minimum value of ( A , B ∈ ( 0 , 4 π ​ ) , A + B sec 2 A + sec 2 B is constant) (r) 2 cos ( A + B ) (d) Minimum value of tan θ + cot θ − 2 cos ( 2 A + 2 B ) ​ ( θ ∈ R , A , B are constants) (s) 2 cos ( A − B )

TestHub · Accepted Answer

(a) cos ( 2 A + θ ) + cos ( 2 B + θ ) = 2 cos ( A + B + θ ) cos ( A − B ) ≤ 2 cos ( A − B ) (s).

List-I	List-II
(a) The maximum value of $cos (2 A + θ) + cos (2 B + θ)$ ( $θ \in R$ and $A, B$ are constants)	(p) $2 sin (A + B)$
(b) Maximum value of $(A, B \in (0, \frac{π}{2}), A + B$ $cos 2 A + cos 2 B$ is constant)	(q) $2 sec (A + B)$
(c) Minimum value of $(A, B \in (0, \frac{π}{4}), A + B$ $sec 2 A + sec 2 B$ is constant)	(r) $2 cos (A + B)$
(d) Minimum value of $tan θ + cot θ - 2 cos (2 A + 2 B)$ ( $θ \in R$ , $A, B$ are constants)	(s) $2 cos (A - B)$

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