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CBSE Class 12 · 2012 · MatricesVery Short Answer

Simplify:

cos θ [cos θ - sin θ sin θ cos θ] + sin θ [sin θ cos θ - cos θ sin θ]

.

Answer: $[1001] = I$

Solution

Multiply each matrix by its scalar and add.

= [cos^{2} θ - sin θ cos θ sin θ cos θ cos^{2} θ] + [sin^{2} θ sin θ cos θ - sin θ cos θ sin^{2} θ] .

Adding entrywise and using

sin^{2} θ + cos^{2} θ = 1

:

= [sin^{2} θ + cos^{2} θ 0 0 sin^{2} θ + cos^{2} θ] = [1001] = I .

CBSE Class 12 Board · 2012 · Subjective

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