What is the general solution for tan(2θ)=(77)/(51-20) ?

The general solution for tan(2θ)=(77)/(51-20) is θ=(1.18805…)/2+(pin)/2

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tan(2θ)=(77)/(51-20)

tan (2 θ) = \frac{77}{51 - 20}

θ = \frac{1.18805 \dots}{2} + \frac{πn}{2}

Solution steps

tan (2 θ) = \frac{77}{51 - 20}

Subtract the numbers:

51 - 20 = 31

tan (2 θ) = \frac{77}{31}

Apply trig inverse properties

2 θ = arctan (\frac{77}{31}) + πn

Solve

2 θ = arctan (\frac{77}{31}) + πn : θ = \frac{arctan ( \frac{77}{31} )}{2} + \frac{πn}{2}

θ = \frac{arctan ( \frac{77}{31} )}{2} + \frac{πn}{2}

Show solutions in decimal form

θ = \frac{1.18805 \dots}{2} + \frac{πn}{2}

2 - 7 cos (x) = 0

cos (θ) = - \frac{8}{17}

cos (2 x) = 8 - 15 sin (x)

sin (4 x) = cos (\frac{x}{2})

a, cos (a - b) = 2

What is the general solution for tan(2θ)=(77)/(51-20) ?
The general solution for tan(2θ)=(77)/(51-20) is θ=(1.18805…)/2+(pin)/2