Answer:
77. 
Proved
78. ![\sec^{4}x \tan^{2} x = \sec^{2}x [\tan^{2}x + \tan^{4}x ]](https://tex.z-dn.net/?f=%5Csec%5E%7B4%7Dx%20%5Ctan%5E%7B2%7D%20x%20%3D%20%5Csec%5E%7B2%7Dx%20%5B%5Ctan%5E%7B2%7Dx%20%2B%20%5Ctan%5E%7B4%7Dx%20%5D)
Proved
79. ![\cos^{3} x\sin^{2} x = [\sin^{2}x - \sin^{4}x] \cos x](https://tex.z-dn.net/?f=%5Ccos%5E%7B3%7D%20x%5Csin%5E%7B2%7D%20x%20%3D%20%5B%5Csin%5E%7B2%7Dx%20-%20%5Csin%5E%7B4%7Dx%5D%20%5Ccos%20x)
Proved.
80. 
Proved.
Step-by-step explanation:
77. Left hand side
= 
= 
= ![\cot^{4}x [\csc^{2}x - 1]](https://tex.z-dn.net/?f=%5Ccot%5E%7B4%7Dx%20%5B%5Ccsc%5E%7B2%7Dx%20-%201%5D)
{Since we know, 
}
= 
= Right hand side (Proved)
78. Left hand side
= 
= ![\sec^{2} x [1 + \tan^{2}x] \tan^{2} x](https://tex.z-dn.net/?f=%5Csec%5E%7B2%7D%20x%20%5B1%20%2B%20%5Ctan%5E%7B2%7Dx%5D%20%5Ctan%5E%7B2%7D%20x)
{Since 
}
= ![\sec^{2}x [\tan^{2}x + \tan^{4}x ]](https://tex.z-dn.net/?f=%5Csec%5E%7B2%7Dx%20%5B%5Ctan%5E%7B2%7Dx%20%2B%20%5Ctan%5E%7B4%7Dx%20%5D)
= Right hand side (Proved)
79. Left hand side
= 
= ![\cos x[1 - \sin^{2} x] \sin^{2} x](https://tex.z-dn.net/?f=%5Ccos%20x%5B1%20-%20%5Csin%5E%7B2%7D%20x%5D%20%5Csin%5E%7B2%7D%20x)
{Since 
}
= ![[\sin^{2}x - \sin^{4}x] \cos x](https://tex.z-dn.net/?f=%5B%5Csin%5E%7B2%7Dx%20-%20%5Csin%5E%7B4%7Dx%5D%20%5Ccos%20x)
= Right hand side
80. Left hand side
= 
= ![[\sin^{2}x + \cos^{2}x]^{2} - 2\sin^{2} x \cos^{2}x](https://tex.z-dn.net/?f=%5B%5Csin%5E%7B2%7Dx%20%2B%20%5Ccos%5E%7B2%7Dx%5D%5E%7B2%7D%20-%202%5Csin%5E%7B2%7D%20x%20%5Ccos%5E%7B2%7Dx)
{Since }
= ![1 - 2\cos^{2} x[1 - \cos^{2}x ]](https://tex.z-dn.net/?f=1%20-%202%5Ccos%5E%7B2%7D%20x%5B1%20-%20%5Ccos%5E%7B2%7Dx%20%5D)
= 
= Right hand side. (Proved)
Answer: 10
Step-by-step explanation:
First you find the median, the middle term (if there are an even number of terms it is the average of the middle two terms.) Since you have 21 terms, odd, you just use the middle term, in this case 8. The first quartile works the same way, but just on the left half between the start and the median...so the first quartile is 6.
As we know these two lines mean | | a modulus sign. The modulus symbol is sometimes used in conjunction with inequalities. A modulus sign in simple words just ignores the sign and gives us the absolute value.
For example in this case the modulus gives us 4 x 2 - 3. As you can see the modulus sign has ignored the original negative signs with the numbers.
So after evaluating the equation the answer comes out to be 8 - 3 which is equal to 5.
