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CBSE Class 12 · 2023 · MatricesLong Answer

If

f (α) = cos α sin α 0 - sin α cos α 0 001

, then prove that

f (α) \cdot f (- β) = f (α - β)

.

Answer: Proved

Solution

Write

f (- β) = cos β - sin β 0 sin β cos β 0 001

(since

cos

is even,

sin

is odd). Multiply:

f (α) f (- β) = cos α cos β + sin α sin β sin α cos β - cos α sin β 0 cos α sin β - sin α cos β sin α sin β + cos α cos β 0 001 .

Using the compound-angle identities, the entries become

cos (α - β)

,

- sin (α - β)

,

sin (α - β)

,

cos (α - β)

:

= cos (α - β) sin (α - β) 0 - sin (α - β) cos (α - β) 0 001 = f (α - β) .

Proved.

CBSE Class 12 Board · 2023 · Subjective

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