All categories

3 years ago

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.

You might be interested in

What is the volume of a hemisphere with a radius of 2.3 m, rounded to the nearest tenth of a cubic meter?

ANTONII [103]

Answer:25.5m^3

Step-by-step explanation:

radius(r)=2.3m

π=3.14

volume of hemisphere=2/3 x π x r^3

Volume=2/3 x 3.14x(2.3)^3

Volume=2/3 x 3.14 x 2.3 x 2.3 x 2.3

volume=(2x3.14x2.3x2.3x2.3) ➗ 3

Volume=76.40876 ➗ 3

Volume=25.5

3 0

3 years ago

Find the midpoint of the line segment with endpoints at the given coordinates (-6,6) and (-3,-9)

JulsSmile [24]

The midpoint of the line segment with endpoints at the given coordinates (-6,6) and (-3,-9) is $\left(\frac{-9}{2}, \frac{-3}{2}\right)$

<u>Solution:</u>

Given, two points are (-6, 6) and (-3, -9)

We have to find the midpoint of the segment formed by the given points.

The midpoint of a segment formed by $\left(\mathrm{x}_{1}, \mathrm{y}_{1}\right) \text { and }\left(\mathrm{x}_{2}, \mathrm{y}_{2}\right)$ is given by:

$\text { Mid point } \mathrm{m}=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)$

$\text { Here in our problem, } x_{1}=-6, y_{1}=6, x_{2}=-3 \text { and } y_{2}=-9$

Plugging in the values in formula, we get,

$\begin{array}{l}{m=\left(\frac{-6+(-3)}{2}, \frac{6+(-9)}{2}\right)=\left(\frac{-6-3}{2}, \frac{6-9}{2}\right)} \\\\ {=\left(\frac{-9}{2}, \frac{-3}{2}\right)}\end{array}$

Hence, the midpoint of the segment is $\left(\frac{-9}{2}, \frac{-3}{2}\right)$

6 0

3 years ago

How can you find the radius of this shape?

V125BC [204]

Answer:

Umm i think yu but it... I would hae to physcally be with you to help you.

Step-by-step explanation:

Sorry. Its hard to explain...

4 0

3 years ago

What expression is equivalent to (^3√2^5)^1/4

Nezavi [6.7K]

Soo first apply the exponent rule (2^5)^1/3*1/4
1/3*1/4= 1/12
so (2^5)^1/12
then you apply the exponent rule again 2^5*1/2
so 5*1/12= 5/12
So the answer would be 2^5/12

6 0

3 years ago

Read 2 more answers

B)the LCM of three numbers is 24 and their G.C.D is 4. If two<br>find the other number

kicyunya [14]

Step-by-step explanation:

because 6*4=24, so the G.C.D is 4 and the other number is 6

4 0

3 years ago