What is the general solution for sin(3x+87)-cos(7x-17)=0 ?

The general solution for sin(3x+87)-cos(7x-17)=0 is x=(4pin+pi-140}{20},x=-\frac{pi+4pin-208)/8

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sin(3x+87)-cos(7x-17)=0

sin (3 x + 87) - cos (7 x - 17) = 0

x = \frac{4 πn + π - 140}{20}, x = - \frac{π + 4 πn - 208}{8}

Solution steps

sin (3 x + 87) - cos (7 x - 17) = 0

Add

cos (7 x - 17)

to both sides

sin (3 x + 87) = cos (7 x - 17)

Rewrite using trig identities

sin (3 x + 87) = sin (\frac{π}{2} - (7 x - 17))

Apply trig inverse properties

3 x + 87 = \frac{π}{2} - (7 x - 17) + 2 πn, 3 x + 87 = π - (\frac{π}{2} - (7 x - 17)) + 2 πn

3 x + 87 = \frac{π}{2} - (7 x - 17) + 2 πn : x = \frac{4 πn + π - 140}{20}

3 x + 87 = π - (\frac{π}{2} - (7 x - 17)) + 2 πn : x = - \frac{π + 4 πn - 208}{8}

x = \frac{4 πn + π - 140}{20}, x = - \frac{π + 4 πn - 208}{8}

sin (20 x) = 0

sin (8 x) + sin (4 x) - 0.5 sin (6 x) = 0

4 sin^{2} (θ) + 4 cos (θ) = 0

cos^{2} (x) = \frac{( 8 k - 9 )}{9}

sin (x) + cot (x) cos (x) = 3

What is the general solution for sin(3x+87)-cos(7x-17)=0 ?
The general solution for sin(3x+87)-cos(7x-17)=0 is x=(4pin+pi-140}{20},x=-\frac{pi+4pin-208)/8