Trig Function Help Please!?

Question

cos(3t)cos(t)=sin(3t)sin(t)

I have gotten all the way to:

(cos t)^4+(sin t)^4=6(sin t)^2(cos t)^2

Could you check that and see if it is right and show me how to get further.

Answer 1

I don't think you are going about this the right way.

cos(3t)cos(t)=sin(3t)sin(t)
cos(3t)cos(t) - sin(3t)sin(t) = 0
cos(3t + t) = 0
cos(4t) = 0
4t = 2n pi +/- pi/2 for any integer n.
t = n pi/2 +/- pi/8.

Answer 2

I can not go further either
cos 3t cos t = sin 3t sin t
tan 3t = cot t
cot t = tan (2t + t ) = cot t
( tan 2t + tan t) / ( 1 - tan 2t tan t ) = cot t
tan 2t + tan t =cot t - tan 2t. tan t / cot t
tan 2t ( 1 + tan t / cot t ) = cot t - tan t
tan 2t ( 1 + sin^2 t / cos^2 t ) = cos t / sin t - sin t / cos t
tan 2t (cos^2 t+sin^2 t )/cos^2 t =(cos^2 t -sin^2 t)/( sin t cos t)
tan 2t /cos^2 t = (1 - 2 sin^2 t ) / ( 1/2 sin 2 t )
tan 2t sin 2t = 2 ( 1 - 2 sin^2 t )
until here only

Answer 3

Cos(a+b) = (cosa)(cosb) -(sina)(sinb)

cos (3t+t) = (cos3t)(cost) - (sin3t)(sint) = 0 as per the the
given identity
4t = +pi/2 or -pi/2
t = + pi/8 or -pi/8

in general you can add or subtract n(2 pi)/4 to the above
answers. ( n=1,2,3 etc.)

Answer 4

cos 3t.cost - sin3t.sint = 0
cos (3t + t) = 0
cos 4t = 0
4t = 90° , 270° , 450° , 630° , 810° , 990°,1170°,1350°
t = 22.5° ,67.5° ,112.5°,157 .5° ,202.5°,
247.5°,292.5°,337.5°

Answer 5

Yes, you are right so far.

Eventually, you should get: cos(4 t) = 0

From there it is easy to solve for t.

Good luck.

Answer 6

im sorry your prob seems complicated!..or could you show the process you went through?