Find one solution for each equation.

1. cos 4theta = sin theta
2. tan 4theta = cot (20^0 + 20)

Write the function sin (B + 35^0) in terms of its cofunction.

cos 4x = sin x

2cos^2 2x - 1 = sin x
2(1 - 2sin^2 x)^2 - 1 = sin x
Now you have to solve a quartic in sin x.

You know from the very 1st equation that
pi/2 is a solution.

The others are not so simple.
Visit wolframalpha.com and enter

solve cos 4x = sin x

to see the graphs and the solutions.