Can I apply the sum-to-product formula to #cos3theta+(sqrt2-1)costheta# and how do I do it?

I'm just wondering how the coefficient before #costheta# will affect the application of the formula.

1 Answer
Nghi N.
Mar 11, 2017

Solve trig equation

Explanation:

I don't understand the question. Do you want to solve or to simplify
the expression? Yes, you can't use sum-to -product trig identity because of the coefficient.
Factor the expression:
Use trig identity:
#cos 3a = cos a(4cos^2 a - 3)#
We get:
#cos 3t + (sqt2 - 1)cos t = cos t(4cos^2 t - 3 + sqrt2 - 1) =#
#= cos t(4cos^2 t - 4+ sqrt2)#
Solve the equation, by using calculator and unit circle -->
a. cos t = 0 --> #t = pi/2#, and #t = (3pi)/2#
b. #(4cos^2 t - 4 + sqrt2) = 0#
#4cos^2 t = 4 - sqrt2 = 2.59#
#cos^2 t = 0.65#
#cos t = +- 0.80#
Calculator, and unit circle give -->
cos t = 0.80 --># t = +- 36^@87#
#cos t = - 0.80# ---> # t = +- 143^@13 #
For general answers , add #2pi = 360^@#

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