Step-by-step explanation:
Left hand side:
4 [sin⁶ θ + cos⁶ θ]
Rearrange:
4 [(sin² θ)³ + (cos² θ)³]
Factor the sum of cubes:
4 [(sin² θ + cos² θ) (sin⁴ θ − sin² θ cos² θ + cos⁴ θ)]
Pythagorean identity:
4 [sin⁴ θ − sin² θ cos² θ + cos⁴ θ]
Complete the square:
4 [sin⁴ θ + 2 sin² θ cos² θ + cos⁴ θ − 3 sin² θ cos² θ]
4 [(sin² θ + cos² θ)² − 3 sin² θ cos² θ]
Pythagorean identity:
4 [1 − 3 sin² θ cos² θ]
Rearrange:
4 − 12 sin² θ cos² θ
4 − 3 (2 sin θ cos θ)²
Double angle formula:
4 − 3 (sin (2θ))²
4 − 3 sin² (2θ)
Finally, apply Pythagorean identity and simplify:
4 − 3 (1 − cos² (2θ))
4 − 3 + 3 cos² (2θ)
1 + 3 cos² (2θ)
Answer:
The domain and range are both x > -4
Step-by-step explanation:
hope it helps have a great day
<em>plz mark brainlest!!</em>
Take the current year and subtract is from the initial year, so
This year is 2016, your are trying to find age if born in 1983
2016
- 1983
-------------
33
You would be 33 years old if you were born in 1983 as of 2016.
Answer: what grade are you in
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Step-by-step explanation:
R = 2 / (1 + sin <span>θ)
Using the following relations:
R = sqrt (x^2 + y^2)
sin </span>θ = y/R
<span>
R = 2 / (1 + y/R)
R</span>(1 + y/R<span>) = 2
</span><span>R + y = 2
R = 2 - y
sqrt(x^2 + y^2) = 2 - y
Squaring both sides:
x^2 + y^2 = (2 - y)^2
x^2 + y^2 = 4 - 4y + y^2
x^2 + 4y - 4
</span>
