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serg [7]
2 years ago
14

If 2tanA=3tanB,then prove that tan(A-B)=sin2B/(5-cos2B) ...?

Mathematics
1 answer:
andreev551 [17]2 years ago
8 0
Tan ( A - B ) = ( tan A - tan B ) / ( 1 + tan A tan B )
tan A = 3 tan B/2
tan ( A - B ) = ((3 tan B/ 2)-tan B) / ( 1 + 3 tan² B/2)=
= (tan B/2)  / ( 2 + 3 sin²B/cos²B )=
= (sin B / cos B) / (( 2cos² B+3sin²B)/cos²B)=
=( sin B cos B ) / ( 2 cos²B + 3 ( 1 - cos² B ) ) =
= (sin B cos B ) / ( 2 cos² B + 3 - 3 cos² B ) =
= ( sin 2 B ) / 2 ( 3 - cos² B ) =
= ( sin 2 B ) / ( 6 - cos² B )=
= ( sin 2 B ) / ( 5 + 1 - 2 cos² B )=
= ( sin 2 B ) / ( 5 + sin² B + cos ² B - 2 cos² B ) =
= ( sin 2 B ) / ( 5 - ( cos² B - sin² B ) ) =
= ( sin 2 B ) / ( 5 - cos 2 B )  - correct 
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2 years ago
F(x) = (x^3)-(3x^2)-3x+1<br> factor please
Anni [7]

Answer:

(x+1)(x²-4x+1)

Step-by-step explanation:

f(x) = x³-3x²-3x+1

     = (x³+1) - 3x (x+1)

     = (x+1)(x²-x+1) - 3x(x+1)

     = (x+1)(x²-x+1-3x)

     = <u>(x+1)(x²-4x+1)</u>

<u />

** (x+1)(x²-4x+1) = (x+1)((x-2)² - 3)

                        = (x+1)((x-2)² - (√3)²)

                        = (x+1)(x-2-√3)(x-2+√3)

5 0
2 years ago
Evaluate the following expressions given x=6 and y=-3
Nana76 [90]

a.

\purple{5 \times 6 - 4 \times ( - 3)}

= 30 + 12

\blue{ =  \boxed{42}}

b.

\purple{ {6}^{2}  +  \frac{6}{ - 3} }

= 36 - 2

\blue{ =  \boxed{34}}

c.

\purple{(6 - 5 {)}^{3}  +  {( - 3)}^{2} }

=  {1}^{3} + 9

= 1 + 9

\blue{ =  \boxed{10}}

<h2>=============================</h2>

Hope it helps

<h2>=============================</h2>
7 0
2 years ago
Explain how to find vertical and horizontal asymptotes of a rational<br> equation.
AleksandrR [38]

Answer:

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If the degree of the numerator is bigger than the denominator, there is no horizontal asymptote.

8 0
3 years ago
Which two terms in (3+14) +27 could you add to get a multiple of ten? ​
Aleksandr-060686 [28]

Answer:

3 and 27

Step-by-step explanation:

<u>Step 1:  Determine which two terms we can use</u>

We have the following numbers to choose from:  3, 14, 27

Adding two numbers to get a multiple of ten means that the number that we come up with needs to be divisible by ten.  For example:  20, 30, 50, 100 are all multiples of ten.

In this example the only one that would add up to create a multiple of ten is 27 and 3 which would give us 30 which is a multiple of 10.

Answer: 3 and 27

8 0
2 years ago
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