If cos² x + sin x = 5/4, then find the value of 'sin x'.
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A.
3/2
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B.
-1/2
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C.
3/4
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D.
1/2
Correct Answer:
D. 1/2
Explanation:
To solve the equation cos² x + sin x = 5/4, first use the trigonometric identity cos² x = 1 - sin² x to rewrite the expression entirely in terms of sine. This gives (1 - sin² x) + sin x = 5/4. By rearranging the terms and multiplying by -1, you get the quadratic equation sin² x - sin x + 1/4 = 0. This expression is a perfect square: (sin x - 1/2)² = 0. Taking the square root of both sides results in sin x - 1/2 = 0, which simplifies to sin x = 1/2. Therefore, the value of sin x that satisfies the original equation is 1/2.
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