Answer:
6/7
Step-by-step explanation:
Answer: see proof below
<u>Step-by-step explanation:</u>
Use the Double Angle Identity: sin 2Ф = 2sinФ · cosФ
Use the Sum/Difference Identities:
sin(α + β) = sinα · cosβ + cosα · sinβ
cos(α - β) = cosα · cosβ + sinα · sinβ
Use the Unit circle to evaluate: sin45 = cos45 = √2/2
Use the Double Angle Identities: sin2Ф = 2sinФ · cosФ
Use the Pythagorean Identity: cos²Ф + sin²Ф = 1
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<u>Proof LHS → RHS</u>
LHS: 2sin(45 + 2A) · cos(45 - 2A)
Sum/Difference: 2 (sin45·cos2A + cos45·sin2A) (cos45·cos2A + sin45·sin2A)
Unit Circle: 2[(√2/2)cos2A + (√2/2)sin2A][(√2/2)cos2A +(√2/2)·sin2A)]
Expand: 2[(1/2)cos²2A + cos2A·sin2A + (1/2)sin²2A]
Distribute: cos²2A + 2cos2A·sin2A + sin²2A
Pythagorean Identity: 1 + 2cos2A·sin2A
Double Angle: 1 + sin4A
LHS = RHS: 1 + sin4A = 1 + sin4A
1/2 is the largest fraction out of all of them
The product has decreased by 80 %
<em><u>Solution:</u></em>
The product of the original numbers: xy
One number is decreased by 75 %
Let x be the number decreased by 75 %
new number = x - 75 % of x
Another number is decreased by 20 %
Let y be the number decreased by 20 %
new number = y - 20 % of y
<em><u>Now the product is given as:</u></em>
<em><u>Now we have to find the percent decreased</u></em>
Subtract new product and original product and then divide by original product . Multiply the result by 100 to get percentage
Here negative sign denotes decrease
Thus the product has decreased by 80 %