can someone help me solve these two equations (and please explain)?

 

log9 (q) = log12 (p) = log18 (q + p)

what is q and what is p?

 

and....

 

sinA + sinB = (square root 2) over 2

cosA + cosB = (square root 6) over 2

sin(A + B) = ?

 

Thanks in advanced!

Sin A + Sin B = 2 Sin((A+B)/2) * Cos((A-B)/2) = sqrt(2)/2 (1)

CosA + CosB = 2Cos((A+B)/2)*Cos((A-B)/2) = sqrt(6)/2 (2)

 

(1)/(2) gives tan((A+B)/2) = 1/sqrt(3)

 

therefore (A+B)/2 = pi/6

 

therefore A+B = pi/3

 

Sin(A+B) = sqrt(3)/2

Are you talking about multiple angle identities?

 

[math]sin(A+B) = sinAcosB + sinBcosA[/math]

 

Also, the question about what is "p and q". They are just a variable for the value of the answer when you put it in the orginal exponent form.

 

i.e. [math]log_{2}p = 3[/math] intends [math]2^{3}=p[/math] and the value of "p" is 8.

p= 24.8638977

q=17.13963918