What is the general solution for cos(7x)=sin(4x+2) ?

The general solution for cos(7x)=sin(4x+2) is x=(-4+4pin+pi}{22},x=-\frac{pi+4pin-4)/6

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cos(7x)=sin(4x+2)

cos (7 x) = sin (4 x + 2)

x = \frac{- 4 + 4 πn + π}{22}, x = - \frac{π + 4 πn - 4}{6}

Solution steps

cos (7 x) = sin (4 x + 2)

Rewrite using trig identities

cos (7 x) = sin (\frac{π}{2} - 7 x)

Apply trig inverse properties

4 x + 2 = \frac{π}{2} - 7 x + 2 πn, 4 x + 2 = π - (\frac{π}{2} - 7 x) + 2 πn

4 x + 2 = \frac{π}{2} - 7 x + 2 πn : x = \frac{- 4 + 4 πn + π}{22}

4 x + 2 = π - (\frac{π}{2} - 7 x) + 2 πn : x = - \frac{π + 4 πn - 4}{6}

x = \frac{- 4 + 4 πn + π}{22}, x = - \frac{π + 4 πn - 4}{6}

12 cos (β) - 5 sin (β) = 4.7

cos (x) = \frac{8}{3}

arctan (θ) = \frac{6}{8}

4 cos^{2} (x) - 7 cos (x) + 3 = 0

tan (θ) = \frac{- \frac{4}{3} - ( - \frac{11}{3} )}{1 + ( - \frac{4}{3} ) ( - \frac{11}{3} )}

What is the general solution for cos(7x)=sin(4x+2) ?
The general solution for cos(7x)=sin(4x+2) is x=(-4+4pin+pi}{22},x=-\frac{pi+4pin-4)/6