If tan2 45° - cos2 60° = x sin 45° cos 45° cot 30°, then find the value of 'x'
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A.
1/ √2
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B.
3/ 2
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C.
√3 / 2
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D.
2 / √3
Correct Answer:
C. √3 / 2
Explanation:
To find the value of x in the equation tan² 45° - cos² 60° = x sin 45° cos 45° cot 30°, substitute the standard trigonometric values: - tan 45° = 1 - cos 60° = 1/2 - sin 45° = 1/√2 - cos 45° = 1/√2 - cot 30° = √3Substitute these into the equation: (1)² - (1/2)² = x \* (1/√2) \* (1/√2) \* √3 Simplify both sides: 1 - 1/4 = x \* (1/2) \* √3 3/4 = x \* (√3/2) Solve for x: x = (3/4) \* (2/√3) x = 3 / (2√3) Rationalize the denominator by multiplying the numerator and denominator by √3: x = (3 \* √3) / (2 \* 3) x = √3 / 2 The value of x is √3 / 2.
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