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प्रश्न
If x sin 60° + cos 30° – tan 45° = `sqrt(3)/2`, find the value of x.
बेरीज
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उत्तर
Given: x sin 60° + cos 30° – tan 45° = `sqrt(3)/2`
Step-wise calculation:
1. Replace the trig values:
`sin 60^circ = sqrt(3)/2`
`cos 30^circ = sqrt(3)/2`
tan 45° = 1
So: `x(sqrt(3)/2) + (sqrt(3)/2) - 1 = sqrt(3)/2`.
2. Subtract `sqrt(3)/2` from both sides:
`x(sqrt(3)/2) + (sqrt(3)/2) - 1 - (sqrt(3)/2) = 0`
⇒ `x(sqrt(3)/2) - 1 = 0`
3. Solve for x:
`x(sqrt(3)/2) = 1`
⇒ `x = 1 ÷ (sqrt(3)/2)`
= `2/sqrt(3)`
4. Rationalize denominator (optional):
`x = 2/sqrt(3) = (2sqrt(3))/3`
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