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:
Step-by-step explanation:
Start with f(x) = √x.
1) Multiplying this by "c" will either stretch or shrink the graph: stretch, if "c" is > 0; shrink, if 0 < c < 1.
2) Replacing 'x' with 'x - h' will translate the original graph h units to the right, if h is positive;
Replacing 'x' with 'x - h' will translate the original graph h units to the left, if h is negative.
3) Adding k to f(x) = √x will translate the graph upward by k units if k is positive and downward by k units if k is negative.
There are 3 girls .
9 students , 3 boys & 3 girls + another 3 boys because there are 3 more than girls so there are only 3 girls since you can't exceed 9 .
Answer:
80
Step-by-step explanation:
Triangles angles measure 180 degrees when added.
You have 2 at 50 which makes 100 degrees.
180 - 100 = 80 degrees
