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Eddi Din [679]
2 years ago
9

Simplify cos^4x+2cos^2xsin^2x+sin^4x

Mathematics
1 answer:
KonstantinChe [14]2 years ago
5 0

Answer: 1

Step-by-step explanation:

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Use the substitution and to rewrite the equations in the system in terms of the variables and . Solve the system in terms of u a
Tatiana [17]

Answer:

x = -1 and y = 1/2

Step-by-step explanation:

Let u = 1/x, and v = 1/y

Then the pair of equations

-3/x + 4/y = 11

1/x - 2/y = -5

Can be written as

-3u + 4v = 11 .................................(1)

u - 2v = -5......................................(2)

From (2)

u = 2v - 5 .......................................(3)

Substituting (3) into (1)

-3(2v - 5) + 4v = 11

-6v + 15 + 4v = 11

-6v + 4v = 11 - 15

-2v = -4

v = 4/2 = 2

Substituting this value of v in (3)

u = 2v - 5

u = 2(2) - 5

= 4 - 5

= -1

That is

u = -1, v = 2

Since u = 1/x, and v = 1/y, we have

1/x = -1

=> x = -1

And

1/y = 2

=> y = 1/2

Therefore

x = -1 and y = 1/2

4 0
3 years ago
Please help me!!!!!​ i need full answer.
salantis [7]

Answer:

see explanation

Step-by-step explanation:

Using the sum/ difference → product formula

cos x - cos y = - 2sin( \frac{x+y}{2})sin (\frac{x-y}{2} )

sin x - sin y = 2cos (\frac{x+y}{2} )sin (\frac{x-y}{2} )

Given

(cosA - cosB)² + (sinA - sinB )²

= [ - 2sin(\frac{A+B}{2})sin(\frac{A-B}{2} ) ]² + [ 2cos(\frac{A+B}{2} )sin(\frac{A-B}{2} ) ]²

= 4sin² (\frac{A+B}{2} )sin² (\frac{A-B}{2} ) + 4cos² (\frac{A+B}{2} )sin² ( \frac{A-B}{2} )

= 4sin² (\frac{A-B}{2} )[ sin² ( \frac{A+B}{2} ) + cos² ( \frac{A+B}{2} ) ← sin²x + cos²x = 1

= 4sin² ( \frac{A-B}{2} ) × 1

= 4sin² ( \frac{A-B}{2} ) = right side ⇒ proven

4 0
3 years ago
(1) 3x + 9 and 5x + 15​
Licemer1 [7]

Answer:

(1)3(x+3)

(2)5(x+3)

Step-by-step explanation:

(1) common taking

(2) common taking

6 0
2 years ago
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6+n-3×6÷9 when n=2<br> this is a mathematical problem
Len [333]

Answer:

6

Step-by-step explanation:

I'm so sorry...i solved this on a calculator so i'm not so sure how to explain once again i'm sorry.

8 0
3 years ago
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Sam wants to get at least an 80% average in his class. He knows that his teacher plans to give five test this marking period. Hi
vesna_86 [32]
Same would need to get at least a 95% on the next test, if he would like to receive a total average of an 80%
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3 years ago
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