What is the general solution for cos(x)-sin(7x)=0 ?

The general solution for cos(x)-sin(7x)=0 is x=(pi+4pin)/(16),x=(pi+4pin)/(12)

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cos(x)-sin(7x)=0

cos (x) - sin (7 x) = 0

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

Solution steps

cos (x) - sin (7 x) = 0

Add

sin (7 x)

to both sides

cos (x) = sin (7 x)

Rewrite using trig identities

cos (x) = sin (\frac{π}{2} - x)

Apply trig inverse properties

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

7 x = \frac{π}{2} - x + 2 πn : x = \frac{π + 4 πn}{16}

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

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

sin (3 x) + sin (x) = 2 sin (2 x)

3 tan (\frac{1}{2} x) + 1 = 0

12 sin (θ) = 4 + 4 sin (θ)

cos (2 x) + cos (8 x) = 0

sin (x) = sin (x) cos (x)

What is the general solution for cos(x)-sin(7x)=0 ?
The general solution for cos(x)-sin(7x)=0 is x=(pi+4pin)/(16),x=(pi+4pin)/(12)