What is the general solution for cos(5x-21)=sin(13-3x) ?

The general solution for cos(5x-21)=sin(13-3x) is x=(4pin+16+pi)/4 ,x=-(pi+4pin-68)/(16)

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cos(5x-21)=sin(13-3x)

cos (5 x - 21) = sin (13 - 3 x)

x = \frac{4 πn + 16 + π}{4}, x = - \frac{π + 4 πn - 68}{16}

Solution steps

cos (5 x - 21) = sin (13 - 3 x)

Rewrite using trig identities

cos (5 x - 21) = sin (\frac{π}{2} - (5 x - 21))

Apply trig inverse properties

13 - 3 x = \frac{π}{2} - (5 x - 21) + 2 πn, 13 - 3 x = π - (\frac{π}{2} - (5 x - 21)) + 2 πn

13 - 3 x = \frac{π}{2} - (5 x - 21) + 2 πn : x = \frac{4 πn + 16 + π}{4}

13 - 3 x = π - (\frac{π}{2} - (5 x - 21)) + 2 πn : x = - \frac{π + 4 πn - 68}{16}

x = \frac{4 πn + 16 + π}{4}, x = - \frac{π + 4 πn - 68}{16}

sin (θ) = \frac{5}{3}

cos (2 θ) + 14 sin^{2} (θ) = 10, 0 < θ < 2 π

14 sin^{2} (x) + 5 sin (x) - 1 = 0

sin (x) = \frac{3}{5} sin (x + \frac{π}{2}) + cos (π - x)

cos (x + π) - sin (x - π) = 0

What is the general solution for cos(5x-21)=sin(13-3x) ?
The general solution for cos(5x-21)=sin(13-3x) is x=(4pin+16+pi)/4 ,x=-(pi+4pin-68)/(16)