Answer:
proved.
Step-by-step explanation:
We have to prove that ![\frac{\sin^{6} x-\cos^{6}x }{1-\sin^{2}x \cos^{2}x } =1-2\cos^{2} x](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csin%5E%7B6%7D%20x-%5Ccos%5E%7B6%7Dx%20%7D%7B1-%5Csin%5E%7B2%7Dx%20%5Ccos%5E%7B2%7Dx%20%20%7D%20%3D1-2%5Ccos%5E%7B2%7D%20x)
So, the left hand side = ![\frac{\sin^{6} x-\cos^{6}x }{1-\sin^{2}x \cos^{2}x }](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csin%5E%7B6%7D%20x-%5Ccos%5E%7B6%7Dx%20%7D%7B1-%5Csin%5E%7B2%7Dx%20%5Ccos%5E%7B2%7Dx%20%20%7D)
=
{Since we have the formula
}
=
{Since we have the formula
}
= ![\frac{(\sin^{2}x-\cos^{2} x )(1-\sin^{2}x \cos^{2}x)}{(1-\sin^{2}x \cos^{2}x)}](https://tex.z-dn.net/?f=%5Cfrac%7B%28%5Csin%5E%7B2%7Dx-%5Ccos%5E%7B2%7D%20x%20%29%281-%5Csin%5E%7B2%7Dx%20%5Ccos%5E%7B2%7Dx%29%7D%7B%281-%5Csin%5E%7B2%7Dx%20%5Ccos%5E%7B2%7Dx%29%7D)
= ![(\sin^{2}x-\cos^{2} x )](https://tex.z-dn.net/?f=%28%5Csin%5E%7B2%7Dx-%5Ccos%5E%7B2%7D%20x%20%29)
=
{Since
}
= Right hand side
Hence, proved.
The answer is C, 6 x 4 = 24!
Answer:
1st is rational 2nd is irrational 3rd is irrational 4th is rational 5th is irrational
Step-by-step explanation:
Step-by-step explanation:
if they are parralel it means gradient is the same
finding equation we find another point which is (x,y)
therefore y - 2/ x - 4 should be equal to 2/3.
y - 2 = 2/3(x - 4)
y - 2 = 2/3x - 8/3
y = 2/3x - 8/3 + 2
Answer:
![cos b=\frac{4}{5}](https://tex.z-dn.net/?f=cos%20b%3D%5Cfrac%7B4%7D%7B5%7D)
Step-by-step explanation:
It is given that: a and b are complementary.
![\therefore a + b = 90\degree\\\\\therefore a = 90\degree - b\\\\Assuming\: sin \: ratio \: on\: both\: sides\\\\sin\:a = sin(90\degree - b)\\\\\therefore \frac{4}{5} = sin(90\degree - b)...(\because sin\:a = \frac{4}{5})\\\therefore \frac{4}{5} =cos\:b...\{\because sin(90\degree - \theta) = cos\: \theta\} \\\\\huge\purple{\boxed{\therefore cos\:b = \frac{4}{5}}}\\](https://tex.z-dn.net/?f=%5Ctherefore%20a%20%2B%20b%20%3D%2090%5Cdegree%5C%5C%5C%5C%5Ctherefore%20a%20%3D%2090%5Cdegree%20-%20b%5C%5C%5C%5CAssuming%5C%3A%20sin%20%5C%3A%20ratio%20%5C%3A%20on%5C%3A%20both%5C%3A%20sides%5C%5C%5C%5Csin%5C%3Aa%20%3D%20sin%2890%5Cdegree%20-%20b%29%5C%5C%5C%5C%5Ctherefore%20%5Cfrac%7B4%7D%7B5%7D%20%3D%20sin%2890%5Cdegree%20-%20b%29...%28%5Cbecause%20sin%5C%3Aa%20%3D%20%5Cfrac%7B4%7D%7B5%7D%29%5C%5C%5Ctherefore%20%5Cfrac%7B4%7D%7B5%7D%20%3Dcos%5C%3Ab...%5C%7B%5Cbecause%20%20sin%2890%5Cdegree%20-%20%5Ctheta%29%20%3D%20cos%5C%3A%20%5Ctheta%5C%7D%20%5C%5C%5C%5C%5Chuge%5Cpurple%7B%5Cboxed%7B%5Ctherefore%20cos%5C%3Ab%20%3D%20%20%5Cfrac%7B4%7D%7B5%7D%7D%7D%5C%5C)