Question -
Answer -
(i) Given
⇒ |A|= x (5x + 1) – (–7) x
|A| = 5x2 + 8x
(ii) Given
⇒ |A|= cos θ × cos θ – (–sin θ) x sin θ
|A| = cos2θ + sin2θ
We know that cos2θ + sin2θ = 1
|A| = 1
(iii) Given
⇒ |A|= cos15° × cos75° + sin15° x sin75°
We know that cos (A – B) = cos A cos B + Sin A sin B
By substituting this we get, |A| = cos (75 – 15)°
|A| = cos60°
|A| = 0.5
(iv) Given
⇒ |A|= (a + ib) (a – ib) – (c + id) (–c + id)
= (a + ib) (a – ib) + (c + id) (c – id)
= a2 – i2 b2 + c2 –i2 d2
We know that i2 = -1
= a2 – (–1) b2 + c2 –(–1) d2
= a2 + b2 + c2 +d2