Question

Solve trigonometric equations:
1) $cos5x=cos(7x-\frac{2\pi }{5} )$
2) $tan(x+\frac{\pi }{6} )=tan(3x-\frac{\pi }{3} )$

Answer 1

cos

θ

=

1

2

θ

=

π

3

,

5

π

3

These are the solutions in the interval \displaystyle \left[0,2\pi \right][0,2π]. All possible solutions are given by

\displaystyle \theta =\frac{\pi }{3}\pm 2k\pi \text{ and }\theta =\frac{5\pi }{3}\pm 2k\piθ=

3

π

±2kπ and θ=

3

5π

±2kπ