Write the left side of the given expression as N/D, where
N = sinA - sin3A + sin5A - sin7A
D = cosA - cos3A - cos5A + cos7A
Therefore we want to show that N/D = cot2A.
We shall use these identities:
sin x - sin y = 2cos((x+y)/2)*sin((x-y)/2)
cos x - cos y = -2sin((x+y)/2)*sin((x-y)2)
N = -(sin7A - sinA) + sin5A - sin3A
= -2cos4A*sin3A + 2cos4A*sinA
= 2cos4A(sinA - sin3A)
= 2cos4A*2cos(2A)sin(-A)
= -4cos4A*cos2A*sinA
D = cos7A + cosA - (cos5A + cos3A)
= 2cos4A*cos3A - 2cos4A*cosA
= 2cos4A(cos3A - cosA)
= 2cos4A*(-2)sin2A*sinA
= -4cos4A*sin2A*sinA
Therefore
N/D = [-4cos4A*cos2A*sinA]/[-4cos4A*sin2A*sinA]
= cos2A/sin2A
= cot2A
This verifies the identity.
Here is the answer hope it helps
Answer:

Step-by-step explanation:
Solve for the value of
:

-Use <u>Distributive Property</u>:


-Combine like terms:


-Take
and subtract it from
:


-Subtract both sides by
:


-Divide both sides by
:


-Reduce the fraction to the lowest term by extracting and canceling out
:


Therefore, the value of
is
.
Answer:
x = -9
Step-by-step explanation:
2x + 8( x + 3 ) = 3( x - 13 )
Dstribute;
2x + 8 ( x + 3 ) = 3 ( x - 13 )
2x + ((8)(x)) + ((8)(3)) = ((3)(x)) - ((13)(3))
2x + 8x + 24 = 3x - 39
Combine like terms;
2x + 8x + 24 = 3x - 39
10x + 24 = 3x - 39
Inverse operations;
10x + 24 = 3x - 39
-3x -3x
7x + 24 = -39
-24 -24
7x = - 63
/7 /7
x = -9