C2→C2−C1
f(θ)=∣−sin2θ−cos2θ12−1−1−211−2∣=4(cos2θ−sin2θ)=4(cos2θ)
Since cos2θ=cos2θ−sin2θ
Again, 4π≤θ≤2π⇒2(4π)≤2θ≤2(2π)
⇒2π≤θ≤π∴θ∈[4π,2π]⇒2θ∈[2π,π] i.e., Second Quadrant.
⇒−1≤cos2θ≤0
f(θ)max=M=0
f(θ)min=m=−4
JEE Main 2020 — Mathematics Algebra
If the minimum and the maximum values of the function f:[4π,2π]→R, defined by f(θ)=∣−sin2θ−cos2θ12−1−sin2θ−1−cos2θ1011−2∣ are m and Mrespectively, then the ordered pair (m,M) is equal to :
Held on 5 Sept 2020 · Verified 6 Jul 2026.
(0,22)
(−4,0)
(−4,4)
(0,4)
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