What is the general solution for 4sin(θ)cos(θ)=1 ?

The general solution for 4sin(θ)cos(θ)=1 is θ= pi/(12)+pin,θ=(5pi)/(12)+pin

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4sin(θ)cos(θ)=1

4 sin (θ) cos (θ) = 1

θ = \frac{π}{12} + πn, θ = \frac{5 π}{12} + πn

Solution steps

4 sin (θ) cos (θ) = 1

Rewrite using trig identities

4 \cdot \frac{sin ( 2 θ )}{2} = 1

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

\frac{sin ( 2 θ ) \cdot 4}{2} = 1

Divide the numbers:

\frac{4}{2} = 2

2 sin (2 θ) = 1

Divide both sides by

2

sin (2 θ) = \frac{1}{2}

General solutions for

sin (2 θ) = \frac{1}{2}

2 θ = \frac{π}{6} + 2 πn, 2 θ = \frac{5 π}{6} + 2 πn

Solve

2 θ = \frac{π}{6} + 2 πn : θ = \frac{π}{12} + πn

Solve

2 θ = \frac{5 π}{6} + 2 πn : θ = \frac{5 π}{12} + πn

θ = \frac{π}{12} + πn, θ = \frac{5 π}{12} + πn

- 64 sin (8 x) = 0

cos (θ) = - 3

tan (θ) = \frac{6}{8}

sec (x) = - 3.5

(sin (x) - 1) = cos (x)

What is the general solution for 4sin(θ)cos(θ)=1 ?
The general solution for 4sin(θ)cos(θ)=1 is θ= pi/(12)+pin,θ=(5pi)/(12)+pin