Answer:
Step-by-step explanation:
sin(x+y) = sin(x)cos(y) + sin(y)cos(x)
sin(x-y) = sin(x)cos(y) - sin(y)cos(x)
Sin(x+y)sin(x-y) = (sin(x)cos(y) + sin(y)cos(x))(sin(x)cos(y) - sin(y)cos(x))
= sin^2(x)cos^2(y) - sin^2(y)cos^2(x)
= sin^2(x)(1-sin^2(y)) - sin^2(y)(1-sin^2(x))
= sin^2(x) - sin^2(x)sin^2(y) - sin^2(y) + sin^2(x)sin^2(y)
= sin^2(x) - sin^2(y)
So L.H.S=R.H.S
Hence proved
7. (4,5) 8. (5,-3) hope that helps
Answer:
a^2 + b^2 = c^2
3^2 + b^2 = 5^2
9 + b^2 = 25
b = _/16
b = 4
Explanation:
Pythagorean Theorem
If Mike has half as many games as Paul, then multiply 6 * 2 to get the number of games that Paul has.
6 * 2 = 12
Paul has 12 games.
I guess you mean
. Since
is in quadrant III, we expect
. Then
![\sin a=-\sqrt{1-\cos^2a}=-\dfrac{\sqrt{21}}5](https://tex.z-dn.net/?f=%5Csin%20a%3D-%5Csqrt%7B1-%5Ccos%5E2a%7D%3D-%5Cdfrac%7B%5Csqrt%7B21%7D%7D5)
Since
is in quadrant I, we expect
, so that
![\sin b=\sqrt{1-\cos^2b}=\dfrac{\sqrt{15}}4](https://tex.z-dn.net/?f=%5Csin%20b%3D%5Csqrt%7B1-%5Ccos%5E2b%7D%3D%5Cdfrac%7B%5Csqrt%7B15%7D%7D4)
Now,
![\sin(a+b)=\sin a\cos b+\cos a\sin b=-\dfrac{2\sqrt{15}+\sqrt{21}}{20}](https://tex.z-dn.net/?f=%5Csin%28a%2Bb%29%3D%5Csin%20a%5Ccos%20b%2B%5Ccos%20a%5Csin%20b%3D-%5Cdfrac%7B2%5Csqrt%7B15%7D%2B%5Csqrt%7B21%7D%7D%7B20%7D)
![\cos(a+b)=\cos a\cos b-\sin a\sin b=\dfrac{3\sqrt{35}-2}{20}](https://tex.z-dn.net/?f=%5Ccos%28a%2Bb%29%3D%5Ccos%20a%5Ccos%20b-%5Csin%20a%5Csin%20b%3D%5Cdfrac%7B3%5Csqrt%7B35%7D-2%7D%7B20%7D)
and
![\tan(a+b)=\dfrac{\sin(a+b)}{\cos(a+b)}=-\dfrac{2\sqrt{15}+\sqrt{21}}{3\sqrt{35}-2}](https://tex.z-dn.net/?f=%5Ctan%28a%2Bb%29%3D%5Cdfrac%7B%5Csin%28a%2Bb%29%7D%7B%5Ccos%28a%2Bb%29%7D%3D-%5Cdfrac%7B2%5Csqrt%7B15%7D%2B%5Csqrt%7B21%7D%7D%7B3%5Csqrt%7B35%7D-2%7D)