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प्रश्न
The maximum value of Δ = `|(1, 1, 1),(1, 1 + sin theta, 1),(1 + cos theta, 1, 1)|` is ______. (θ is real number)
विकल्प
`1/2`
`sqrt(3)/2`
`sqrt(2)`
`(2sqrt(3))/4`
उत्तर
The maximum value of Δ = `|(1, 1, 1),(1, 1 + sin theta, 1),(1 + cos theta, 1, 1)|` is `1/2`. (θ is real number)
Explanation:
Δ = `|(1, 1, 1),(1, 1 + sin theta, 1),(1 + cos theta, 1, 1)|`
[Applying C1 → C1 – C1 and C2 → C2 – C3]
= `|(0, 0, 1),(0, sin theta, 1),(cos theta, 0, 1)|`
= – sin θ · cos θ
= `-1/2 * 2 sin theta cos theta`
= `- 1/2 sin 2theta`
So, maximum value of Δ is `1/2` when sin 2θ = –1.
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