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3 years ago

Prove the identity cos(x-y)-cos(x+y)=2sinxsiny

Mathematics

1 answer:

tekilochka [14]3 years ago

7 0

Answer:

see the procedure

Step-by-step explanation:

we know that

$cos(X - Y) = cosX cosY + sinX sinY\\cos(X + Y) = cosX cosY - sinX sinY$

$cos(X - Y)-cos(X + Y)=cosX cosY + sinX sinY-(cosX cosY - sinX sinY)$

$cos(X - Y)-cos(X + Y)=cosX cosY + sinX sinY-cosX cosY + sinX sinY$

$cos(X - Y)-cos(X + Y)=sinX sinY+ sinX sinY$

$cos(X - Y)-cos(X + Y)=2sinX sinY$ ----> is verified

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A triangle has sides with lengths of 5 meters, 12 meters, and 13 meters. Is it a right triangle?

Setler [38]

Answer:

yes :

use the following formula :

a^2 +b^2 = c^2

now apply it to the problem :

5^2+12^2=13^2

do the exponent :

25 + 144 =169

now add

169 =169

if they are equal , then it is a right triangle .

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3 years ago

What is the ratio (multiplier) for the following geometric sequence? 2, 0.5, 0.125, .03125...

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3 years ago

a water balloon is tossed into the air with an upward velocity of 25 ft/s its height h(t) in ft after t seconds is given by the

Montano1993 [528]

When the height is 0 that is when it hits the ground
solve
0=-16t²+25x+3
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for
0=ax²+bx+c
$x=\frac{-b+/-\sqrt{b^2-4ac}}{2a}$

so for
0=-16t²+25t+3
a=-16
b=25
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so

$x=\frac{-25+/-\sqrt{25^2-4(-16)(3)}}{2(-16)}$
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$x=\frac{-25+/-\frac{817}}{-32}$
it has to be a positive time

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3 years ago

A. 11/1=165/h B. 11/1=h/165 C. 132/12=h/165 D=12/132=165/h plz help

Hunter-Best [27]

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Hope dis helps! :D

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3 years ago

How can you determine if you need to use a combination or permutation to count the number of outcomes? Which will usually have m

Nadya [2.5K]

Answer with Step-by-step explanation:

Permutation : It is an arrangement of r elements out of n elements.

Combination : it is a selection of r element out of n elements .

Suppose we have a set

S={1,2,3}

If two elements are taken at a time then

Using permutation formula

Total number of outcomes= $3P_2$

Total number of outcomes= $\frac{3!}{(3-2)!}$

Total number of outcomes=3!= $3\times 2\times1=6$

Using combination formula

$\binom{n}{r}=\frac{n!}{r!(n-r)!}$

Total number of outcomes= $\binom{3}{2}=\frac{3!}{2!1!}$

Total number of outcomes= $\frac{3\times2!}{2!}$

Hence, total number of outcomes=3

Total number of outcomes determined by permutation have more outcomes.

Because permutation is an arrangement of elements therefore, it consider order of arrangement of element but combination is a selection of elements it does no consider order of elements

Arrangements of two elements out of 3 elements

{1,2},{2,3},{2,1},{3,2},{1,3},{3,1}

By using combination if two elements taken at a time then combination

{1,2},{2,3},{1,3}

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3 years ago