What is the general solution for cos(2x)=sin(70+x) ?

The general solution for cos(2x)=sin(70+x) is x=(3240n+180}{27},x=-\frac{180+3240n)/9

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cos(2x)=sin(70+x)

cos (2 x) = sin (7 0^{\circ} + x)

x = \frac{324 0 ^{\circ} n + 18 0 ^{\circ}}{27}, x = - \frac{18 0 ^{\circ} + 324 0 ^{\circ} n}{9}

Solution steps

cos (2 x) = sin (7 0^{\circ} + x)

Rewrite using trig identities

cos (2 x) = sin (9 0^{\circ} - 2 x)

Apply trig inverse properties

7 0^{\circ} + x = 9 0^{\circ} - 2 x + 36 0^{\circ} n, 7 0^{\circ} + x = 18 0^{\circ} - (9 0^{\circ} - 2 x) + 36 0^{\circ} n

7 0^{\circ} + x = 9 0^{\circ} - 2 x + 36 0^{\circ} n : x = \frac{324 0 ^{\circ} n + 18 0 ^{\circ}}{27}

7 0^{\circ} + x = 18 0^{\circ} - (9 0^{\circ} - 2 x) + 36 0^{\circ} n : x = - \frac{18 0 ^{\circ} + 324 0 ^{\circ} n}{9}

x = \frac{324 0 ^{\circ} n + 18 0 ^{\circ}}{27}, x = - \frac{18 0 ^{\circ} + 324 0 ^{\circ} n}{9}

tan (3 x) \cdot cot (x + 4 0^{\circ}) = 1

2 cos (θ) + 53 = 43

cos (x) = - \frac{1}{2} 2

sin (x) = - cos^{2} (x) - 1, 0 \leq x \leq 2 π

sin (x) (tan (x) - 3) = 0

What is the general solution for cos(2x)=sin(70+x) ?
The general solution for cos(2x)=sin(70+x) is x=(3240n+180}{27},x=-\frac{180+3240n)/9