Step-by-step explanation:
(1 + cos θ + sin θ) / (1 + cos θ − sin θ)
Multiply by the reciprocal:
(1 + cos θ + sin θ) / (1 + cos θ − sin θ) × (1 + cos θ + sin θ) / (1 + cos θ + sin θ)
(1 + cos θ + sin θ)² / [ (1 + cos θ − sin θ) (1 + cos θ + sin θ) ]
(1 + cos θ + sin θ)² / [ (1 + cos θ)² − sin² θ) ]
Distribute and simplify:
(1 + cos θ + sin θ)² / (1 + 2 cos θ + cos² θ − sin² θ)
[ 1 + 2 (cos θ + sin θ) + (cos θ + sin θ)² ] / (1 + 2 cos θ + cos² θ − sin² θ)
(1 + 2 cos θ + 2 sin θ + cos² θ + 2 sin θ cos θ + sin² θ) / (1 + 2 cos θ + cos² θ − sin² θ)
Use Pythagorean identity:
(2 + 2 cos θ + 2 sin θ + 2 sin θ cos θ) / (sin² θ + cos² θ + 2 cos θ + cos² θ − sin² θ)
(2 + 2 cos θ + 2 sin θ + 2 sin θ cos θ) / (2 cos² θ + 2 cos θ)
(1 + cos θ + sin θ + sin θ cos θ) / (cos² θ + cos θ)
Factor:
(1 + cos θ + sin θ (1 + cos θ)) / (cos θ (1 + cos θ))
(1 + cos θ)(1 + sin θ) / (cos θ (1 + cos θ))
(1 + sin θ) / cos θ
Answer:
45
Step-by-step explanation:
Answer:
You got it wrong. It is supposed to be (1, -4)
Step-by-step explanation:
If you are not sure, just plug it in. So based on this you got that x= -6.
So plug x=-6 into the first equation. -6= -y-3. So you solve for y.
You add 3 to both sides and get that -3= -y and y=3, so you did not get it correct because you got that y=-4. So you may be asking, how do you do this?
So first, you already know that x=-y-3. So you substitute that into the 2nd equation for x. That gets you -2(-y-3)-y=2. Use distributive property and get 2y+6-y=2. Combine like terms and subtract 6 from both sides to get y= -4.
Now you substitute y=-4 into any equation, I'll just use the first equation. X= -(-4)-3. That gets x= 4-3. That gets x= 1
Answer:
2
Explanation
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The required solution of the inequality is x < - 6.
Given that,
To solve the equation −2x − 4 > 8.
<h3>What is inequality?</h3>
Inequality can be described as the consideration of the equation including the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
The given equation
−2x − 4 > 8
adding 4 on both sides
-2x > 12
multiply by -1
when multiplying the negative -1 it will change the behavior of the inequality, so.
2x < - 12
Divide by 2 into both sides
x < - 6
Thus, the required solution of the inequality is x < - 6.
Learn more about inequality here:
brainly.com/question/14098842
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