Question

Solve the equation for cos theta-tan theta=0 for greater than or egual to zero but less than 2pi. Write your answer as a multiple of pi, if possible form the following choices:
pi , 5pi
A. --- ----
4___ 4
B. pi 3pi 5pi 7pi
----- '----- '-----'-----
4_____ 4_____ 4______4

C. pi 3pi 3pi 7pi
----- '----- '-----'-----
2_______4______2_____4

D. pi 7pi 3pi 11pi
----- '----- '-----'-----
2________6______2_____6

Answer 1

cos ( theta ) - tan ( theta) = 0

tan ( theta ) = sin (theta ) / cos( theta )

cos ( theta ) - tan ( theta ) =0

cos ( theta ) = tan ( theta )

cos ( theta ) = sin ( theta ) / cos ( theta )

cos^2 ( theta) = sin ( theta )

Now go on:

wolframalpha dot com

When page be open in rectangle type :

solve cos^2 ( theta) = sin ( theta )

and click =

After few seconds you will see solution.

Then click option Show steps

Answer 2

cosØ - tanØ = 0
cosØ - sinØ/cosØ = 0
multiply by cosØ
cos^2Ø - sinØ = 0
(1 - sin^2Ø) - sinØ = 0
sin^2Ø + sinØ - 1 = 0
sinØ = (-1 ± √5)/2
sinØ = .618034 or -1.608 , the last is not possible since sinØ has to be between -1 and +1
Ø = 38.17° from my calculator (or 141.83°)

All your choices are in radians in multiples of π/2, π/4 or π/6
which would be multiples of 90°, 45° or 30°

None of these match,

btw, my answers satisfies the original equation.