Trigonometry (1 Viewer)

[R0L13D]

Can someone help me with this question?
cos3x + cos5x + cos7x = 0, in the domain [0,pi]
Surely, there’s a simpler way; rather than expanding the whole left hand side.

 

[TheShy]

was there something before this question? I've seen the cos3x cos 5x cos7x in one of the cosAcosB=1/2 (cos(A-B) .... whatever the formula is

 

[R0L13D]

I also need help with this q?
The answer says 576 but I got 864. Can someone please explain where I went wrong?

 

[TheShy]

_ _ _ _ _ _ _ _. 8 seats to sit on. Mariya must be in seat 1 and Aofa can't be in seat 8, so for now we will put her on the second seat:
M A _ _ _ _ _ _. Then you got the 3 ppl that gotta be together so :
M A c m h _ _ _ _. For those 3 ppl, they have 4 patterns in which they can sit, and they can be arranged in 3!, so can the other 3 random ppl. So you got 4 x 3! x 3! Then we also gotta consider Asofa since he/she can also sit in the 7th or 6th seat or whatever seat but the last: This means she can sit in the 2nd, 3rd, 4th, 5th, 6th and 7th seat, so 6 seats she can sit in total
therefore: 4 x 3! x 3! x 6 = 864

 

[R0L13D]

_ _ _ _ _ _ _ _. 8 seats to sit on. Mariya must be in seat 1 and Aofa can't be in seat 8, so for now we will put her on the second seat:
M A _ _ _ _ _ _. Then you got the 3 ppl that gotta be together so :
M A c m h _ _ _ _. For those 3 ppl, they have 4 patterns in which they can sit, and they can be arranged in 3!, so can the other 3 random ppl. So you got 4 x 3! x 3! Then we also gotta consider Asofa since he/she can also sit in the 7th or 6th seat or whatever seat but the last: This means she can sit in the 2nd, 3rd, 4th, 5th, 6th and 7th seat, so 6 seats she can sit in total
therefore: 4 x 3! x 3! x 6 = 864

I did that but it’s 576 apparently

 

[tito981]

I did that but it’s 576 apparently

place mariya in seat 1, think of cooper, manny and hafsa as one 'person', so now there are 5 effective people, there are only 4 possibilities for seat 8, then there is 4! for the rest of the seats. Then multiply by 3! for coop, manny and hafsa. so it is 4x4!x3!=576.