Answer:
what is the question you only gave the problem
Step-by-step explanation:
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>
Answer:
The range of numbers that Nidhi might be thinking of is between 3 and 9.
Step-by-step explanation:
We are given that Nidhi is thinking of a number n, and she wants her sister to guess the number.
Her first clue is that eight less than three times her number is between one and nineteen.
Let the number Nidhi is thinking be 'n'.
So, eight less than three times her number means that;
Now, according to the question; the above equation is between one and nineteen, so;
Adding 8 to the whole expression;
Dividing the whole expression by 3;
Hence, the range of numbers that Nidhi might be thinking of is between 3 and 9.
The greatest perimeter of a rectangle with an area of 39 ft.² is 78
