The answer for this is -12
Answer
12. x = 15, y = 21
13. x = 10, M = 37, N = 84, P =59
14. x = 19, R = 43, S = 20, T = 117
15. A = 21, B = 125, C = 34
16. J = 48, K = 57, L = 75
Explanation
12. 6x - 11 + x + 5 + 81 = 180
7x + 75 = 180
7x = 105
x = 15
4y - 18 + y + 14 + 6*15 - 11 = 180
5y + 75 = 180
5y = 105
y = 21
13. 4x - 3 + 9x - 6 + 6x - 1 = 180
19x - 10 = 180
19x = 190
x = 10
M = 4*10 - 3 = 37
N = 9*10 - 6 = 84
P = 6*10 - 1 = 59
14. R = 2x + 5
S = x + 1
T = 7x - 16
2x + 5 + x + 1 + 7x - 16 = 180
10x - 10 = 180
10x = 190
x = 19
R = 2*19 + 5 = 43
S = 19 + 1 = 20
T = 7*19 -16
15. A = C -13
B = 4C - 11
c - 13 + 4c - 11 + c = 180
6c -24 = 180
6c = 2-4
C = 34
A = 34 - 13 = 21
B = 4*34 - 11 = 125
16. K = J + 9
L = 2J -21
j + 9 + 2j - 21 + j = 180
4j -12 = 180
4j = 192
J = 48
K = 48 + 9 = 57
L = 2*48 -21 = 75
Answer:
6
Step-by-step explanation:
x+6-10=2
x+6=12
x=12-6
<h2>x=6 </h2>
<h3>hence the number is 6</h3>
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)
