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

The general solution for sin(7x)=cos(2x) is x=(pi+4pin)/(18),x=(pi+4pin)/(10)

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sin(7x)=cos(2x)

sin (7 x) = cos (2 x)

x = \frac{π + 4 πn}{18}, x = \frac{π + 4 πn}{10}

Solution steps

sin (7 x) = cos (2 x)

Rewrite using trig identities

sin (7 x) = sin (\frac{π}{2} - 2 x)

Apply trig inverse properties

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

7 x = \frac{π}{2} - 2 x + 2 πn : x = \frac{π + 4 πn}{18}

7 x = π - (\frac{π}{2} - 2 x) + 2 πn : x = \frac{π + 4 πn}{10}

x = \frac{π + 4 πn}{18}, x = \frac{π + 4 πn}{10}

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

sec^{2} (x) csc (x) - 2 csc (x) = 2 - sec^{2} (x)

2 sin (x) = - 2, 0 \leq x \leq 2 π

csc (a) = 3

csc (a) = 5

What is the general solution for sin(7x)=cos(2x) ?
The general solution for sin(7x)=cos(2x) is x=(pi+4pin)/(18),x=(pi+4pin)/(10)