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Trigonometric Identities (G12)

question 1 of 12 Grade: Twelve - G12

Q: The product-to-sum formula states that \(\sin A \cos B = \frac{1}{2}[\sin(A+B) + \sin(A-B)]\).

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For equal roots, the discriminant must be zero: \(D = b^2 - 4ac = 0\). Here \(a = 1\), \(b = 4\), \(c = k\), so \(4^2 - 4(1)(k) = 0\) ⇒ \(16 - 4k = 0\) ⇒ \(4k = 16\) ⇒ \(k = 4\). Therefore, the statement is correct.

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Did You Know?

For equal roots, the discriminant must be zero: \(D = b^2 - 4ac = 0\). Here \(a = 1\), \(b = 4\), \(c = k\), so \(4^2 - 4(1)(k) = 0\) ⇒ \(16 - 4k = 0\) ⇒ \(4k = 16\) ⇒ \(k = 4\). Therefore, the statement is correct.

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