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Serggg [28]
3 years ago
9

How do you simplify sin^4-cos^4=2sin^2-1?

Mathematics
1 answer:
Naily [24]3 years ago
8 0

\bf \textit{Double Angle Identities} \\\\ cos(2\theta)= \begin{cases} cos^2(\theta)-sin^2(\theta)\\ 1-2sin^2(\theta)\\ 2cos^2(\theta)-1 \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}

\bf \begin{array}{llll} sin^4(\theta )-cos^4(\theta )&=&2sin^2(\theta )-1\\[1em] [sin(\theta )]^4-[cos(\theta )]^4&=&-[1-2sin^2(\theta )]\\[1em] \stackrel{\textit{difference of squares}}{[[sin(\theta )]^2]^2-[[cos(\theta )]^2]^2}&=&-[cos^2(\theta )-sin^2(\theta )]\\[1em] [sin^2(\theta )-cos^2(\theta )][sin^2(\theta )+cos^2(\theta )]&=&sin^2(\theta )-cos^2(\theta )\\[1em] [sin^2(\theta )-cos^2(\theta )][1]&=\\\\ sin^2(\theta )-cos^2(\theta ) &=\end{array}

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Consider the exponential equation 4^x = 30. Between what two consecutive integers must the solution to this equation lie? Explai
Alex_Xolod [135]

Answer:

2 and 3.

Step-by-step explanation:

Four to the second power is 16.

Four to the third power is 64.

30 lies between 16 and 64, thus the exponent must lie between 2 and 3.

7 0
3 years ago
What is the value of x?
Ray Of Light [21]
96 and (6x - 36) are alternate exterior angles, meaning that they are equal to each other.

6x - 36 = 96

Add 36 to both sides.

6x = 132

Divide by 6 on both sides.

x = 22

The value of x is 22.
4 0
3 years ago
A circle has a radius of 26.85 inches. What is the circumference of this circle? Use 3.14 for pi. Round your final answer to the
Ad libitum [116K]

Answer:

Step-by-step explanation:

Circumference of the circle = 2 x pi x r

= 2 x 3.14 x 26.85

= 168.618 Inches

after rounding to nearest tenth, 168.6 inches

5 0
3 years ago
Read 2 more answers
. The perimeter of a square is 8y – 12. The area of the square is 100 square units. What is the value of y?
evablogger [386]

Answer:

y = 6.5 units

Step-by-step explanation:

Let L be the length of sides of the square.

Given the following data;

Perimeter of square = 8y - 12

Area of square = 100 square units

To find the value of y;

Area of a square = L²

Substituting into the formula, we have;

100 = L²

L = √100

L = 10 units

Mathematically, the perimeter of a square is given by the formula;

Perimeter of a square = 4L

Substituting into the formula, we have;

8y - 12 = 4*10

8y - 12 = 40

8y = 40 + 12

8y = 52

y = 52/8

y = 6.5 units

6 0
3 years ago
Read 2 more answers
Write the decimal in fractional notation: 0.097 A 97/1000 B 97/10,000 C 970 /1000 D 97/10
jeyben [28]
If you would like to write 0.097 in fractional notation, you can do this like this:

0.097 = 97 / 1000 

The correct result would be <span>A 97/1000.</span>
3 0
4 years ago
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