Compute the following-i - a b- -b a - a b- b a - ii - a2-b2 b2-c2- a2-c2 a2-b2 - 2 a b 2 b c- -2 a c -2 a b -iii - -1 4 -6- 8 5 16- 2 8 5 - 12 7 6- 8 0 5- 3 2 4 -v - cos 2 x sin 2 x- sin 2 x cos 2 x - sin 2 x cos 2 x- cos 2 x sin 2 x -

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BODMAS

Compute the f...

Question

Compute the following:

(i) (ii)

(iii)

(v)

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[\begin{matrix} a & b - b & a \end{matrix}] + [\begin{matrix} a & b b & a \end{matrix}]

[\begin{matrix} a^{2} + b^{2} & b^{2} + c^{2} a^{2} + c^{2} & a^{2} + b^{2} \end{matrix}] + [\begin{matrix} 2 a b & 2 b c - 2 a c & - 2 a b \end{matrix}]

⎡ ⎢ ⎣ \begin{matrix} - 1 82 \end{matrix} \begin{matrix} 458 \end{matrix} \begin{matrix} - 6 165 \end{matrix} ⎤ ⎥ ⎦ + ⎡ ⎢ ⎣ \begin{matrix} 1283 \end{matrix} \begin{matrix} 702 \end{matrix} \begin{matrix} 654 \end{matrix} ⎤ ⎥ ⎦

[\begin{matrix} {cos}^{2} x & {sin}^{2} x {sin}^{2} x & {cos}^{2} x \end{matrix}] + [\begin{matrix} {sin}^{2} x & {cos}^{2} x {cos}^{2} x & {sin}^{2} x \end{matrix}]

(a^{2} - b^{2}) (b^{2} + c^{2}) = (b^{2} - c^{2}) (a^{2} + b^{2})

a (b^{2} + c^{2}) = c (a^{2} + b^{2})

If A = $[\begin{matrix} a & b b & a \end{matrix}]$ and $A^{2}$ = $[\begin{matrix} x & y y & x \end{matrix}]$ , then

Δ A B C

c o s A = \frac{b^{2} + c^{2} - a^{2}}{2 b c}, c o s B = \frac{c^{2} + a^{2} - b^{2}}{2 a c}, c o s C = \frac{a^{2} + b^{2} - c^{2}}{2 a b}

If a + b + c = 2s, then prove the following identities

(a) s² + (s − a)² + (s − b)² + (s − c)² = a² + b² + c²

(b) a² + b² − c² + 2ab = 4s (s − c)

(d) a² − b² − c² + 2ab = 4(s − b) (s − c)

(e) (2bc + a² − b² − c²) (2bc − a² + b² + c²) = 16s (s − a) (s − b) (s − c)

(f)

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