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प्रश्न
The maximum value of `|(1, 1, 1),(1, (1 + sintheta), 1),(1, 1, 1 + costheta)|` is `1/2`
विकल्प
True
False
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उत्तर
This statement is True.
Explanation:
Let Δ = `|(1, 1, 1),(1, (1 + sintheta), 1),(1, 1, 1 + costheta)|`
C1 → C1 – C2, C2 → C2 – C3
= `|(0, 0, 1),(-sintheta, sintheta, 1),(0, -costheta, 1 + costheta)|`
Expanding along C3
= `1|(-sintheta, sintheta),(0, -costheta)|`
= sin θ cos θ – 0
= sin θ cos θ
= `1/2 * 2 sin theta cos theta`
= `1/2 sin 2theta`
= `1/2 xx 1` ......[Maximum value of sin 2θ = 1]
= `1/2`
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