Prove the identity (8 tan theta)/(1+tan^2 theta)=4 sin 2 theta

Is this an identity?

b) Complete an identity for cos^4 x-sin^4 x
1. cos^4 x-sin^4 x=4cos x-4sin x
2. cos^4 x-sin^4 x=1
3. cos^4 x-sin^4 x=sin^2 2x
4. cos^4 x-sin^4 x=2cos^2 x-1

c) Simplify. (9cot t csc t+3csc t)/6cot t csc t-3csc t)
1. (2csc t+1)/(3csc t-1)
2. (3csc t-1)/(2csc t+1)
3. (3csc t+1)/(2csc t-1)
4. (2csc t-1)/(3csc t+1)

d) Find an equivalent expression for sin^4 x in terms of function values of the sine or cosine of x, 2x, or 4x raised to the first power.
1. (sin^2 x)^2
2. sin 4x
3. (1/4)-(1/2)cos 2x+(cos^2 2x/4)
4. (3/8)-(cos 2x/2)+(cos 4x/8)

e) Given that cos theta=60/61 and theta is in Quadrant IV, determine sin 2(theta), cos 2(theta), and tan 2(theta). Which quadrant is 2(theta) in?
1. sin 2(theta)=
2. cos 2(theta)=
3. tan 2(theta)=
Choose the quadrant that 2(theta) is in:
1. IV
2. II
3. I

f) Factor and simplify.
tan^3 x+8=?

g) Use a double-angle or half-angle identity to simplify (2-sec^2 x)/(sec^2 x).
1. cos 2x
2. 2cos^2 x-1
3. 1
4. (sec 2x)/(sec^2 x)

h) Given that sin theta= 1/8 and that the terminal side is in quadrant I, find exact answers for cos(pi/2-theta) and cos(theta+pi/2)
1. cos(pi/2-theta)=
2. cos(theta+pi/2)=

i) Determine if the equation is an identity (cot x-tan x)/(sec x csc x)=1. Yes or No?

j) Write the expression as a trigonometric function of a single angle. Then evaluate.
sin 40degrees cos 28degrees+ cos 40degrees sin 28degrees

k) Find the exact value of tan 3pi/8 using the half-angle identity.
tan 3pi/8=

l) Use a sum-to-product identity to rewrite the expression.
cos 3a+ cos 8a=

m) Find the exact value of tan(a+B) if sin a=0.1102 and cos B=0.4111, and both a and B are first-quadrand angles.
tan(a+B)=

n) Simplify. Assume that all function values in radicans are nonnegative. sqroot(cos a sin^4 a)-sq root(cos^7 a).