What is the general solution for cos(7a)=sin(a-6) ?

The general solution for cos(7a)=sin(a-6) is a=(12+4pin+pi)/(16),a=-(pi+4pin+12)/(12)

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cos(7a)=sin(a-6)

cos (7 a) = sin (a - 6)

a = \frac{12 + 4 πn + π}{16}, a = - \frac{π + 4 πn + 12}{12}

Solution steps

cos (7 a) = sin (a - 6)

Rewrite using trig identities

cos (7 a) = sin (\frac{π}{2} - 7 a)

Apply trig inverse properties

a - 6 = \frac{π}{2} - 7 a + 2 πn, a - 6 = π - (\frac{π}{2} - 7 a) + 2 πn

a - 6 = \frac{π}{2} - 7 a + 2 πn : a = \frac{12 + 4 πn + π}{16}

a - 6 = π - (\frac{π}{2} - 7 a) + 2 πn : a = - \frac{π + 4 πn + 12}{12}

a = \frac{12 + 4 πn + π}{16}, a = - \frac{π + 4 πn + 12}{12}

sin^{5} (x) + 2 cos^{2} (x) = 1

cos^{3} (x) + sin^{2} (x) = 0

cos^{22} (x) + sin^{2} (x) - 1 = 0

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

sin (x) cos (x^{2}) = 0

What is the general solution for cos(7a)=sin(a-6) ?
The general solution for cos(7a)=sin(a-6) is a=(12+4pin+pi)/(16),a=-(pi+4pin+12)/(12)