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प्रश्न
Without using tables, evaluate the following: sin230° sin245° + sin260° sin290°.
उत्तर
sin230° sin245° + sin260° sin290°
sin30° = `(1)/(2)`
sin45° = `(1)/sqrt(2)`
sin60° = `sqrt(3)/(2)`
sin90° = 1
sin230° sin245° + sin260° sin290°
= `(1/2)^2 (1/sqrt(2))^2 + (sqrt(3)/2)^2 1`
= `(1)/(4) xx (1)/(2) + (3)/(4)`
= `(1)/(8) + (3)/(4)`
= `(1 + 6)/(8)`
= `(7)/(8)`.
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