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>
![\bf 2sin(x)cos(x)=sin(x)\sqrt{2}\implies 2sin(x)cos(x)-sin(x)\sqrt{2}=0 \\\\\\ sin(x)~[2cos(x)-\sqrt{2}]=0\\\\ -------------------------------\\\\ sin(x)=0\implies \measuredangle x=0~~,~~\pi \\\\ -------------------------------\\\\ 2cos(x)-\sqrt{2}=0\implies 2cos(x)=\sqrt{2}\implies cos(x)=\cfrac{\sqrt{2}}{2} \\\\\\ \measuredangle x=\frac{\pi }{4}~~,~~\frac{7\pi }{4}](https://tex.z-dn.net/?f=%5Cbf%202sin%28x%29cos%28x%29%3Dsin%28x%29%5Csqrt%7B2%7D%5Cimplies%202sin%28x%29cos%28x%29-sin%28x%29%5Csqrt%7B2%7D%3D0%0A%5C%5C%5C%5C%5C%5C%0Asin%28x%29~%5B2cos%28x%29-%5Csqrt%7B2%7D%5D%3D0%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C%0Asin%28x%29%3D0%5Cimplies%20%5Cmeasuredangle%20x%3D0~~%2C~~%5Cpi%20%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C%0A2cos%28x%29-%5Csqrt%7B2%7D%3D0%5Cimplies%202cos%28x%29%3D%5Csqrt%7B2%7D%5Cimplies%20cos%28x%29%3D%5Ccfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Cmeasuredangle%20x%3D%5Cfrac%7B%5Cpi%20%7D%7B4%7D~~%2C~~%5Cfrac%7B7%5Cpi%20%7D%7B4%7D)
now, we're not including the III and II quadrants, where the cosine has an angle of the same value, but is negative, because the exercise seems to be excluding the negative values of √(2).
Answer:
QRST becomes Q prime, R prime, S prime, T prime.
Step-by-step explanation:
Any figure that is rotated, translated or reflected on the corrdinate plane is considered a prime (as long as it is congruent (the same as, or equal to) with the original). The apostrophe stands for prime.
Ex. If you reflect triangle ABC across one of the axes, the original triangle will continue being ABC, while the reflection would be A' B' C' (or A prime, B prime, C prime). I hope this helps :)
A₅=6*5-4
a₅=30-4
a₅=26
D. 26
Good Studies!!
