1) To find the exact value of sin 165 degrees, we can use the sum of angles formula for sine, which is:
sin (A + B) = sin A * cos B + cos A * sin B
In this case, we can rewrite 165 degrees as 120 degrees + 45 degrees. Now we can find the sine and cosine values of each angle and apply the formula:
sin 120 = sqrt(3)/2
cos 120 = -1/2
sin 45 = sqrt(2)/2
cos 45 = sqrt(2)/2
Now, we apply the formula:
sin 165 = sin(120 + 45) = sin 120 * cos 45 + cos 120 * sin 45
sin 165 = (sqrt(3)/2) * (sqrt(2)/2) + (-1/2) * (sqrt(2)/2)
sin 165 = (sqrt(6) + sqrt(2))/4
The exact value of sin 165 degrees is (sqrt(6) + sqrt(2))/4.
2) To simplify the expression (4m/5n^2) - (n/2m), we first find the common denominator, which is 10n^2m. Then, we combine the expressions:
(4m/5n^2)*(2m/2m) - (n/2m)*(5n^2/5n^2)
(8m^2/10n^2m) - (5n^3/10n^2m)
Now, we can combine the numerators:
(8m^2 - 5n^3)/10n^2m
Thus, the simplified expression is (8m^2 - 5n^3)/10n^2m.
1)Find the exact value of sin 165 degrees.
Answer: (sqrt6 + sqrt2)/4
2) Simplify: (4m/5n^2)- (n/2m)
Answer: (8m^2-5n^3)/10n^2m
Thanks
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