Compute the following-cos - 2 x -sin- 2 x lsin- 2 x -cos - 2 xendbmatrix - Weginbmatrix sin - 2 x -cos- 2 xcos - 2 x -sin- 2 x llendbmatrix

[ cos^2 x amp; sin^2 x; sin^2 x amp; cos^2 x ] +[ sin^2 x amp; cos^2 x; cos^2 x amp; sin^2 x; ] =[ cos^2 x+sin^2 x amp; si ...

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Compute the f...

Question

Compute the following:
$(i v) [\begin{matrix} c o s^{2} x & s i n^{2} x s i n^{2} x & c o s^{2} x \end{matrix}] + [\begin{matrix} s i n^{2} x & c o s^{2} x c o s^{2} x & s i n^{2} x \end{matrix}]$

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\int \frac{s i n^{2} x - c o s^{2} x}{s i n^{2} x c o s^{2} x} d x

c o s 4 x = 1 - 8 s i n^{2} x c o s^{2} x

f (x) = ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 + s i n^{2} x & c o s^{2} x & 4 s i n 2 x s i n^{2} x & 1 + c o s^{2} x & 4 s i n 2 x s i n^{2} x & c o s^{2} x & 1 + 4 s i n 2 x \end{matrix} ∣ ∣ ∣ ∣ ∣

f (x) =

x

∣ ∣ ∣ ∣ \begin{matrix} cos 2 x & sin 2 x & sin 2 x sin 2 x & cos 2 x & sin 2 x sin 2 x & sin 2 x & cos 2 x \end{matrix} ∣ ∣ ∣ ∣ = 0

x ϵ [0, \frac{π}{4}]

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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