What is the general solution for sin(θ)csc(3θ-40)=1,calculetan(3θ) ?

The general solution for sin(θ)csc(3θ-40)=1,calculetan(3θ) is No Solution for θ\in\mathbb{R}

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sin(θ)csc(3θ-40)=1,calculetan(3θ)

sin (θ) csc (3 θ - 40) = 1, c a l c u l e tan (3 θ)

No Solution for θ \in R

Solution steps

sin (θ) csc (3 θ - 40) = 1, c a l c u l e tan (3 θ)

Subtract

1

from both sides

sin (θ) csc (3 θ - 40) - 1 = 0

Express with sin, cos

\frac{- sin ( - 40 + 3 θ ) + sin ( θ )}{sin ( - 40 + 3 θ )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

- sin (- 40 + 3 θ) + sin (θ) = 0

Rewrite using trig identities

2 cos ((- 10 + θ) \cdot 2) sin (20 - θ) = 0

Solving each part separately

cos ((- 10 + θ) \cdot 2) = 0 or sin (20 - θ) = 0

cos ((- 10 + θ) \cdot 2) = 0, c a l c u l e tan (3 θ) :

No Solution

sin (20 - θ) = 0, c a l c u l e tan (3 θ) :

No Solution

Combine all the solutions

No Solution for θ \in R

3 cot^{2} (x) - 4 cot (x) + 3 = 0

cos^{2} (x) + 5 cos (x) - 6 = 0

10 sin (x) = 4 cos^{2} (x) + 2

- 4 + sin (- 3 x + \frac{2 π}{3}) = - 4

2 \cdot sin (x) \cdot cos (x) = cos (x)

What is the general solution for sin(θ)csc(3θ-40)=1,calculetan(3θ) ?
The general solution for sin(θ)csc(3θ-40)=1,calculetan(3θ) is No Solution for θ\in\mathbb{R}