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प्रश्न
Evaluate the following in the simplest form:
sin 60° cos 30° + cos 60° sin 30°
Evaluate the following:
sin 60° cos 30° + cos 60° sin 30°
उत्तर १
sin 60° cos 30° + cos 60° sin 30°
= `\frac{\sqrt{3}}{2}\times \frac{\sqrt{3}}{2}+\frac{1}{2}\times\frac{1}{2}`
= `\frac{3}{4}+\frac{1}{4}`
= 1
उत्तर २
sin 60° cos 30° + cos 60° sin 30° ...(i)
By trigonometric ratios we have,
`sin 60° = sqrt3/2 sin 30°`
= `1/2`
`cos 30° = sqrt3/2 cos 60°`
= `1/2`
Substituting above values in (i), we get
`sqrt3/2 . sqrt3/2 + 1/2 . 1/2`
= `3/4 + 1/4`
= `4/4`
= 1
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