What is the general solution for 2cos(a)sin(a)-4cos(a)+6sin(a)-12=0 ?

The general solution for 2cos(a)sin(a)-4cos(a)+6sin(a)-12=0 is No Solution for a\in\mathbb{R}

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Popular >

2cos(a)sin(a)-4cos(a)+6sin(a)-12=0

Solution

2 cos (a) sin (a) - 4 cos (a) + 6 sin (a) - 12 = 0

Solution

No Solution for a \in R

Solution steps

2 cos (a) sin (a) - 4 cos (a) + 6 sin (a) - 12 = 0

Factor

2 cos (a) sin (a) - 4 cos (a) + 6 sin (a) - 12 : 2 (sin (a) - 2) (cos (a) + 3)

2 cos (a) sin (a) - 4 cos (a) + 6 sin (a) - 12

Rewrite

- 12

6 \cdot 2

Rewrite

6

3 \cdot 2

= 2 sin (a) cos (a) + 2 \cdot 2 cos (a) + 3 \cdot 2 sin (a) + 3 \cdot 2 \cdot 2

Factor out common term

2

= 2 (sin (a) cos (a) - 2 cos (a) + 3 sin (a) - 6)

Factor

sin (a) cos (a) + 3 sin (a) - 2 cos (a) - 6 : (sin (a) - 2) (cos (a) + 3)

sin (a) cos (a) + 3 sin (a) - 2 cos (a) - 6

= (sin (a) cos (a) - 2 cos (a)) + (3 sin (a) - 6)

Factor out

3

from

3 sin (a) - 6 : 3 (sin (a) - 2)

3 sin (a) - 6

Rewrite

- 6

2 \cdot 3

= 3 sin (a) + 2 \cdot 3

Factor out common term

3

= 3 (sin (a) - 2)

Factor out

cos (a)

from

sin (a) cos (a) - 2 cos (a) : cos (a) (sin (a) - 2)

sin (a) cos (a) - 2 cos (a)

Factor out common term

cos (a)

= cos (a) (sin (a) - 2)

= 3 (sin (a) - 2) + cos (a) (sin (a) - 2)

Factor out common term

sin (a) - 2

= (sin (a) - 2) (cos (a) + 3)

= 2 (sin (a) - 2) (cos (a) + 3)

2 (sin (a) - 2) (cos (a) + 3) = 0

Solving each part separately

sin (a) - 2 = 0 or cos (a) + 3 = 0

sin (a) - 2 = 0 :

No Solution

sin (a) - 2 = 0

Move

2

to the right side

sin (a) - 2 = 0

Add

2

to both sides

sin (a) - 2 + 2 = 0 + 2

Simplify

sin (a) = 2

sin (a) = 2

- 1 \leq sin (x) \leq 1

No Solution

cos (a) + 3 = 0 :

No Solution

cos (a) + 3 = 0

Move

3

to the right side

cos (a) + 3 = 0

Subtract

3

from both sides

cos (a) + 3 - 3 = 0 - 3

Simplify

cos (a) = - 3

cos (a) = - 3

- 1 \leq cos (x) \leq 1

No Solution

Combine all the solutions

No Solution for a \in R

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for 2cos(a)sin(a)-4cos(a)+6sin(a)-12=0 ?
The general solution for 2cos(a)sin(a)-4cos(a)+6sin(a)-12=0 is No Solution for a\in\mathbb{R}