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प्रश्न
The value of (sin 30° + cos 30°)2 – (sin 60° – cos 60)2 is ______.
रिक्त स्थान भरें
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उत्तर
The value of (sin 30° + cos 30°)2 – (sin 60° – cos 60)2 is `underlinebb(sqrt(3))`.
Explanation:
Let `sin 30^circ = 1/2, cos 30^circ = sqrt(3)/2`
`sin 60^circ = sqrt(3)/2, cos 60^circ = 1/2`
Then `(sin 30^circ + cos 30^circ)^2 = ((1 + sqrt(3))/2)^2 = 1 + sqrt(3)/2`
`(sin 60^circ - cos 60^circ)^2 = ((sqrt(3) - 1)/2)^2 = 1 - sqrt(3)/2`
Subtracting gives `(1 + sqrt(3)/2) - (1 - sqrt(3)/2) = sqrt(3)`
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