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
Answer:
15
Step-by-step explanation:
A third of 45 is 1/3 multiplied by 45 or 45 divided by 3, which is equal to 15.
You would use the law of cosines
![\mathbb P(142](https://tex.z-dn.net/?f=%5Cmathbb%20P%28142%3CX%3C174%29%3D%5Cmathbb%20P%5Cleft%28%5Cdfrac%7B142-142%7D%7B16%7D%3C%5Cdfrac%7BX-142%7D%7B16%7D%3C%5Cdfrac%7B174-142%7D%7B16%7D%5Cright%29%3D%5Cmathbb%20P%280%3CZ%3C2%29)
Approximately 95% of any normal distribution lies within two standard deviations of the mean, i.e.
![\mathbb P(-2](https://tex.z-dn.net/?f=%5Cmathbb%20P%28-2%3CZ%3C2%29%5Capprox0.95)
. Because the distribution is symmetric, you have
![\mathbb P(-2](https://tex.z-dn.net/?f=%5Cmathbb%20P%28-2%3CZ%3C2%29%3D2%5Cmathbb%20P%280%3CZ%3C2%29)
, so
![\mathbb P(0](https://tex.z-dn.net/?f=%5Cmathbb%20P%280%3CZ%3C2%29%5Capprox%5Cdfrac%7B0.95%7D2%3D0.475%5Capprox0.48)
.