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Anton [14]
3 years ago
11

Prove that sin^4x - cos^4x = 2sin^2x - 1

Mathematics
1 answer:
Liula [17]3 years ago
5 0

Step-by-step explanation:

Step 1: From the given equation, taking the Left Hand Side (LHS) of the equation

Step 2: Simplify the LHS to make it equal to the Right Hand Side (RHS)

LHS = sin^4x - cos^4x = (sin²x)² - (cos²x)²

       = (sin²x - cos²x)(sin²x + cos²x)

       = sin²x - (1 - sin²x)  since sin²x + cos²x = 1

       = 2 sin²x - 1

       = RHS

Hence proved.

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If h(x)=6-x what is the value of (h•h)(110)
Irina18 [472]

The given function : h(x) = 6 - x

We know that for any functions f(x) and g(x)

f*g (x)=f(x)\times g(x)

Therefore , h*h (x)=h(x)\times h(x)

h*h (x)=(6-x)(6-x)=(6-x)^2

h*h (x)=(6)^2-2(6)(x)+x^2 [ Using identity   (a-b)^2=a^2+2ab+b^2 ]

h*h (x)=36-12(x)+x^2

\-------->\ h*h (x)=36-12(x)+x^2 Now, at x= 10 , we get

h*h (10)=36-12(10)+(10)^2

h*h (10)=36-120+100=36+100-120=136-120=16

Hence, the value of (h*h)(10) = 16

hoped it helped

8 0
2 years ago
Pleasee help<br><br> 15 points
Nostrana [21]

Answer:

10

Step-by-step explanation:

4 0
2 years ago
See image for question.​
kotegsom [21]

Answer:

<h3>#7</h3>

(a)

<u>Sample space:</u>

  • 1*1, 1*2, 1*3, 1*4,
  • 2*1, 2*2, 2*3, 2*4,
  • 3*1, 3*2, 3*3, 3*4,
  • 4*1, 4*2, 4*3, 4*4

Total 16 outcomes

(b)

  • (i) P(even) = 12/16 = 3/4
  • (ii) P(3x) = 7/16
  • (iii) P(perfect square) = 4/16 = 1/4
<h3>#8</h3>

(a) <u>Sample space:</u>

  • 1T, 1H, 2T, 2H, 3T, 3H, 4T, 4H

Total 8 outcomes

(b)

(i) 1T, 3T

  • P(T and odd) = 2/8 = 1/4

(ii) 1H, 4H

  • P(H and square) = 2/8 = 1/4

(iii) 1H, 2H, 3H, 4H

  • P(H) = 4/8 = 1/2

6 0
3 years ago
Chris earns a fixed amount of money every month. At the end of 2 years, chris had earned $86,688. He earned $ each year. He earn
dmitriy555 [2]

Answer:

Chris earned $ 43,344 each year

Monthly Chris earns $ 3,612

Step-by-step explanation:

If you earn a fixed amount of money each month, for 2 years and one year you have 12 months, then 2 years equals 24 months.

To know how much you earn each month we divide the total amount earned in the two years between 24 months

I = $ 86,688 / 24

I = $ 3,612

Monthly Chris earns $ 3,612


To calculate what he earned each year we divided $ 86,688 / 2

I = $ 86,688 / 2

I = $ 43,344

Chris earned $ 43,344 each year

6 0
3 years ago
A public health department charges $25.00 for a flu shot.The vaccine costs $0.78 per shot, a syringe costs $0.51, and the labor
AlladinOne [14]

The cost of a single shot is

.78 +.52 +.96 = 2.26

they charge 25 a shot

25 - 2.26 = 22.74

there is a profit of 22.74 per shot

22.74 * 167 =3797.58

They make $3797.58

5 0
3 years ago
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