Question

Sin50*sin15=   sin33*cos 47=   sin12*cos8*cos10=   sin15*cos45=   cos75*sin105=

Answer 1

0,19

0,37

0,20

0,18

0,25

 

 

Answer 2

To calculate these trigonometric expressions, we can use the trigonometric identities and properties. Let's evaluate each expression step by step:

1. sin(50) * sin(15): Using the identity sin(A) * sin(B) = (1/2) * [cos(A - B) - cos(A + B)], we can rewrite the expression as: sin(50) * sin(15) = (1/2) * [cos(50 - 15) - cos(50 + 15)] = (1/2) * [cos(35) - cos(65)]

2. sin(33) * cos(47): Using the identity sin(A) * cos(B) = (1/2) * [sin(A + B) + sin(A - B)], we can rewrite the expression as: sin(33) * cos(47) = (1/2) * [sin(33 + 47) + sin(33 - 47)] = (1/2) * [sin(80) + sin(-14)] = (1/2) * [sin(80) - sin(14)] [since sin(-x) = -sin(x)]

3. sin(12) * cos(8) * cos(10): Using the identity sin(A) * cos(B) = (1/2) * [sin(A + B) + sin(A - B)], we can rewrite the expression as: sin(12) * cos(8) * cos(10) = (1/2) * [sin(12 + 8 + 10) + sin(12 - 8 - 10)] = (1/2) * [sin(30) + sin(-6)] = (1/2) * [sin(30) - sin(6)] [since sin(-x) = -sin(x)]

4. sin(15) * cos(45): Using the identity sin(A) * cos(B) = (1/2) * [sin(A + B) + sin(A - B)], we can rewrite the expression as: sin(15) * cos(45) = (1/2) * [sin(15 + 45) + sin(15 - 45)] = (1/2) * [sin(60) + sin(-30)] = (1/2) * [sin(60) - sin(30)] [since sin(-x) = -sin(x)]

5. cos(75) * sin(105): Using the identity cos(A) * sin(B) = (1/2) * [sin(A + B) - sin(A - B)], we can rewrite the expression as: cos(75) * sin(105) = (1/2) * [sin(75 + 105) - sin(75 - 105)] = (1/2) * [sin(180) - sin(-30)] = (1/2) * [sin(180) + sin(30)] [since sin(-x) = -sin(x)]

Please note that I've used the trigonometric identities to rewrite the expressions. Now you can evaluate the expressions using a calculator or trigonometric tables to get the numerical values.