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)
-13 -23 because divide by two then add five and subtract 5
Answer: Area of cross section that is parallel to face CDHG is 432 cm².
Step-by-step explanation:
Since we have given that
There is a cross section that is parallel to face CDHG.
So, Length of cross section would be 36 cm
Width of cross section would be 12 cm.
So, Area of cross section would be
Hence, Area of cross section that is parallel to face CDHG is 432 cm².
8) red and 1, red and 2, red and 3, blue and 1, blue and 2, blue and 3
So answer is 6
9) 0.5*1/3 = 0.17
10) 0.5*2/3 = 0.33
