Let fx-sin 2x-sin 2x-2 cos - sin x- sin x- Which of the following is TRUE about fx -

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Standard Limits to Remove Indeterminate Form

Let fx=sin 2x...

Question

Let $f (x) = {sin}^{2} (x + α) + {sin}^{2} (x + β) - 2 cos (α - β) sin (x + α) sin (x + β)$ .Which of the following is TRUE about $f (x)$ ?

f(x) is strictly increasing in

x \in (α, β)

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f(x) is strictly decreasing in

x \in (α, β)

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f(x) is strictly increasing in

x \in (α, \frac{α + β}{2})

and strictly decreasing in

x \in (\frac{α + β}{2}, β)

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f(x) is a constant function

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f (x) = ∣ ∣ ∣ ∣ ∣ \begin{matrix} cos (x + α) + i sin (x + α) & cos (x + β) + i sin (x + β) & cos (x + γ) + i sin (x + γ) sin (x + α) - i cos (x + α) & sin (x + β) - i cos (x + β) & sin (x + γ) - i cos (x + γ) sin (2 β - 2 γ) & sin (2 γ - 2 α) & sin (2 α - 2 β) \end{matrix} ∣ ∣ ∣ ∣ ∣

f (α) + f (β) - 2 f (γ)

f (x) = ∣ ∣ ∣ ∣ ∣ \begin{matrix} cos (x + α) & cos (x + β) & cos (x + γ) sin (x + α) & sin (x + β) & sin (x + γ) sin 2 α & sin 2 β & sin 2 γ \end{matrix} ∣ ∣ ∣ ∣ ∣

α, β, γ

2 f (\frac{π}{4}) - 3 f (\frac{π}{6}) + f (\frac{π}{3})

f (x) = \frac{1 - sin 2 x + cos 2 x}{2 cos 2 x}

α + β = \frac{5 π}{4} .

f (α) \cdot f (β)

f (x) = ∣ ∣ ∣ ∣ ∣ \begin{matrix} cos (x + α) & cos (x + β) & cos (x + γ) sin (x + α) & sin (x + β) & sin (x + γ) sin (β - γ) & sin (γ - α) & sin (α - β) \end{matrix} ∣ ∣ ∣ ∣ ∣

α, β, γ \in R

f (0) = - 2,

30 \sum r = 1 | f (r) |

sin 2 x = α - 1

cos 2 x = β - 1

\frac{{sec}^{2} x [({cos}^{2} x - {sin}^{2} x) - 2 sin x cos x]}{1 + sin 2 x}

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