Let f(x)=| sin 2 x -2+ cos 2 x cos 2 x 2+ sin 2 x cos 2 x cos 2 x sin 2 x cos 2 x 1+ cos 2 x |, x ∈[0, π] Then the maximum value of f(x) is equal to

Question

Let f(x)=| sin 2 x -2+ cos 2 x cos 2 x 2+ sin 2 x cos 2 x cos 2 x sin 2 x cos 2 x 1+ cos 2 x |, x ∈[0, π] Then the maximum value of f(x) is equal to (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

|-2 -2 0 2 0 -1 sin 2 x cos 2 x 1+ cos 2 x| (R1 arrow R1-R2 R2 arrow R2-R3) -2( cos 2 x)+2(2+2 cos 2 x+ sin 2 x) 4+4 cos 2 x-2( cos 2 x- sin 2 x) f(x)=4+ undersetmax = 12 cos 2 x f(x) max =4+2=6

Q. Let $f (x) = ∣ ∣ sin^{2} x 2 + sin^{2} x sin^{2} x - 2 + cos^{2} x cos^{2} x cos^{2} x cos 2 x cos 2 x 1 + cos 2 x ∣ ∣,$
$x \in [0, π]$ Then the maximum value of $f (x)$ is equal to

$∣ ∣ - 2 2 sin^{2} x - 2 0 cos^{2} x 0 - 1 1 + cos 2 x ∣ ∣$
$(R_{1} \to R_{1} - R_{2} & R_{2} \to R_{2} - R_{3})$
$- 2 (cos^{2} x) + 2 (2 + 2 cos 2 x + sin^{2} x)$
$4 + 4 cos 2 x - 2 (cos^{2} x - sin^{2} x)$
$f (x) = 4 + ma x = 1 2 cos 2 x$
$f (x)_{m a x} = 4 + 2 = 6$

Q. Let f(x)=∣∣​sin2x2+sin2xsin2x​−2+cos2xcos2xcos2x​cos2xcos2x1+cos2x​∣∣​, x∈[0,π] Then the maximum value of f(x) is equal to

∣∣​−22sin2x​−20cos2x​0−11+cos2x​∣∣​ (R1​→R1​−R2​&R2​→R2​−R3​) −2(cos2x)+2(2+2cos2x+sin2x) 4+4cos2x−2(cos2x−sin2x) f(x)=4+max=12cos2x​ f(x)max​=4+2=6

Q. Let $f (x) = ∣ ∣ sin^{2} x 2 + sin^{2} x sin^{2} x - 2 + cos^{2} x cos^{2} x cos^{2} x cos 2 x cos 2 x 1 + cos 2 x ∣ ∣,$
$x \in [0, π]$ Then the maximum value of $f (x)$ is equal to

$∣ ∣ - 2 2 sin^{2} x - 2 0 cos^{2} x 0 - 1 1 + cos 2 x ∣ ∣$
$(R_{1} \to R_{1} - R_{2} & R_{2} \to R_{2} - R_{3})$
$- 2 (cos^{2} x) + 2 (2 + 2 cos 2 x + sin^{2} x)$
$4 + 4 cos 2 x - 2 (cos^{2} x - sin^{2} x)$
$f (x) = 4 + ma x = 1 2 cos 2 x$
$f (x)_{m a x} = 4 + 2 = 6$