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Pani-rosa [81]
3 years ago
9

Prove the identity (cosx+cosy)^2+(sinx-siny)^2= 2+2cos(x+y)

Mathematics
2 answers:
muminat3 years ago
8 0
TRIGONOMETRIC \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: RESOLUTIONS \\ \\ \\\\Given \: expression \: - \\ \\ \\ { (\cos(x) + \cos(y)} )^{2} + ( {( \sin(x ) - \sin(y) )}^{2} \\ \\ = { \cos(x) }^{2} + { \cos(y) }^{2} + 2 \cos(x) \cos(y) \\ \: \: \:+\: \: { \sin(x) }^{2} + { \sin(y) }^{2} - 2 \sin(x) \sin(y) \\ \\ = { \cos(x) }^{2} \: + { \sin(x) }^{2} + \\ \: \: \: \: \: { \cos(y) }^{2} + { \sin(x) }^{2} \: + \\ \: \: \: \: \: 2( \cos(x) \cos(y) - \sin(x) \sin(y) ) \\ \\ = \: 1 + 1 + 2( \cos(x + y) ) \\ \\ Using \:Trigonometric \: Identities \: - \\ \\ { \sin(q) }^{2} + { \cos(q) }^{2} = \: 1 \: \\ \cos(x) \cos(y) - \sin(x) \sin(y) = \cos(x + y) \\ \\ \\ \\ { (\cos(x) + \cos(y)} )^{2} + ( {( \sin(x ) - \sin(y) )}^{2} \\ = 2 + 2( \cos(x + y) ) \: \: \: \: \: \: \: \: \: \: \: \: \: \: Ans.\\ \\
astra-53 [7]3 years ago
4 0
(cos(x) + cos(y))^2 + (sin(x) - sin(y))^2 Remove the brackets

cos^2(x)
+ cos^2(y) + 2cos(x)*cos(y) + sin^2(x) - 2(sin(x)*sin(y) + sin^2(y) Combine these two in bold to make 1 because sin^2(x) + cos^2(x) = 1

1 + cos^2(y) + 2cos(x)*cos(y) - 2*sin(x)*cos(y) + sin^2(y) 
These two in bold also make 1

2 + 2cos(x)*cos(y) - 2*sin(X)*sin(y) Bring out a common factor of 2
2 +2(cos(x)*cos(y) -  sin(x)*sin(y) )

but cos(x+y ) = cos(x)*cos(y) - sin(x)*sin(y)

2 + 2* cos(x + y) is your final answer. 

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slava [35]

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▹ Answer

<em>3 × 4 = 4 × 3</em>

▹ Step-by-Step Explanation

You can use any expression that shows the commutative property of multiplication. For example, 3 × 4 = 4 × 3

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4 0
2 years ago
On Friday a bowling alley made $842.72 from Lane rentals in $412.38 from the concession stand.
Neko [114]

Answer:

d

Step-by-step explanation:

8 0
2 years ago
Michael made 4 dozen chocolate chip cookies he is bringing 75% of them to school for a party how many cookies does he bring to c
olga2289 [7]
12 cookies= 1 dozen.
12*4 (dozens) =48
48/ 4= 12
12 cookies is a 1/4 or 25% of the whole amount of cookies. 
48- 12= 36
He brings 36 cookies to school. 
4 0
2 years ago
Estimate <br><img src="https://tex.z-dn.net/?f=%20%5Csqrt%7B80%7D%20" id="TexFormula1" title=" \sqrt{80} " alt=" \sqrt{80} " ali
Tamiku [17]

Answer:

8.9

Step-by-step explanation:

Convert  √ 80  to a decimal.

8.9442719

Find the number in the tenth place  9  and look one place to the right for the rounding digit  4 . Round up if this number is greater than or equal to  5  and round down if it is less than  5 .

8 0
3 years ago
Factorise fully : 6x²-11x-10 ​
steposvetlana [31]

Answer:

After factorization we got,

(6x + 5)(x  - 2)

Step-by-step explanation:

here's the solution: -

=》

6 {x}^{2}  - 7x - 10

=》

6 {x}^{2}  - 12x + 5x - 10

=》

6x(x - 2) + 5(x - 2)

=》

(6x + 5)(x - 2)

7 0
3 years ago
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