The answer in itself is 1/128 and here is the procedure to prove it:
cos(A)*cos(60+A)*cos(60-A) = cos(A)*(cos²60 - sin²A)
<span>= cos(A)*{(1/4) - 1 + cos²A} = cos(A)*(cos²A - 3/4) </span>
<span>= (1/4){4cos^3(A) - 3cos(A)} = (1/4)*cos(3A) </span>
Now we group applying what we see above
<span>cos(12)*cos(48)*cos(72) = </span>
<span>=cos(12)*cos(60-12)*cos(60+12) = (1/4)cos(36) </span>
<span>Similarly, cos(24)*cos(36)*cos(84) = (1/4)cos(72) </span>
<span>Now the given expression is: </span>
<span>= (1/4)cos(36)*(1/4)*cos(72)*cos(60) = </span>
<span>= (1/16)*(1/2)*{(√5 + 1)/4}*{(√5 - 1)/4} [cos(60) = 1/2; </span>
<span>cos(36) = (√5 + 1)/4 and cos(72) = cos(90-18) = </span>
<span>= sin(18) = (√5 - 1)/4] </span>
<span>And we seimplify it and it goes: (1/512)*(5-1) = 1/128</span>
1/3
there are two red spots on the spinner and six spots all together. the fraction would be 2/6, reduced would be 1/3 the decimal answer would be 0.333 repeating.
Answer:
45
Step-by-step explanation:
Answer:
7/24
Step-by-step explanation:
3/8 is changed to 9/24 people lifting weights
1/3 is changed to 8/24 people cross training
17/24 people are not running
7/24 people are running
7/24 cannot be reduced
Answer:
10 rides
Step-by-step explanation:
Make an equation.
25 + 2x = 35 + 1x
Subract 1x from the 2x to get 1.
New Equation: 25 + 1x = 35
Subtract 25 from 35 to get 10.
New Equation: 1x = 10
Divide 1 from both sides.
Answer: 10 rides
