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:
Linear function 2x+3y=12 .
Step-by-step explanation:
To find y-intercept , make x=0 :
3y = 12
y = 12/3
y = 4 .
To find x-intercept , make y=0 :
2x = 12
x = 12/2
x = 6 .
<u> ! Hope this will help you !</u>
Writing this problem in symbols instead of in words greatly simplifies it:
(2 2/3) * (1 1/5) * (1 1/2)
Write each quantity (inside each set of parentheses) as an improper fraction:
(8/3) * (6/5) * (3/2)
Now multiply the numerators thru: 8*6*3 / 3*5*2
Notice that we can reduce this by dividing the 8 by the 2 and dividing the 6 by the 3: 4*3*3 36
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5 5