If x ∈[0,2 π], a, b, c ∈ R(t 0) such that √1+ sin 2 x+|t+(4/t)-4|+(a+b+c)2 ≤ 0, then the value of | sin x - cos x t t 2 sin x cos x a3+b3+c3 3 a b c a2+b2+c2|

Question

If x ∈[0,2 π], a, b, c ∈ R(t> 0) such that √1+ sin 2 x+|t+(4/t)-4|+(a+b+c)2 ≤ 0, then the value of | sin x - cos x t t 2 sin x cos x a3+b3+c3 3 a b c a2+b2+c2| (A) depend upon a, b, c (B) depend upon x (C) depend upon (D) independent of a, b, c, x and t

Tardigrade Admin · Accepted Answer

1+ sin 2 x=0, t+(4/t)-4=0, a+b+c=0 ⇒ sin x+ cos x=0, t=2 use C1 arrow C1-C2, we get |ccc0 - cos x t 0 2 sin x cos x 0 3 a b c a2+b2+c2|=0

Q. If $x \in [0, 2 π], a, b, c \in R (t > 0)$ such that
$1 + sin 2 x + ∣ ∣ t + \frac{4}{t} - 4 ∣ ∣ + (a + b + c)^{2} \leq 0$ , then the value of $∣ ∣ sin x t a^{3} + b^{3} + c^{3} - cos x 2 3 ab c t sin x cos x a^{2} + b^{2} + c^{2} ∣ ∣$

depend upon $a, b, c$

depend upon $x$

depend upon

independent of $a, b, c, x$ and $t$

$1 + sin 2 x = 0, t + \frac{4}{t} - 4 = 0, a + b + c = 0$
$\Rightarrow sin x + cos x = 0, t = 2$
use $C_{1} \to C_{1} - C_{2}$ , we get
$∣ ∣ ccc 0 00 - cos x 2 3 ab c t sin x cos x a^{2} + b^{2} + c^{2} ∣ ∣ = 0$

Q. If x∈[0,2π],a,b,c∈R(t>0) such that 1+sin2x​+∣∣​t+t4​−4∣∣​+(a+b+c)2≤0, then the value of ∣∣​sinxta3+b3+c3​−cosx23abc​tsinxcosxa2+b2+c2​∣∣​

depend upon a,b,c

depend upon x