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Alenkinab [10]
2 years ago
12

Tan 2A + sin 2A=4 tan A/(1 - tan4 A)​

Mathematics
1 answer:
stich3 [128]2 years ago
3 0

Answer:

when \:  \\  \tan(2x)  =   \frac{2 \tan(x) }{1 -  {( \tan(x)) }^{2} }  \:  \: and \\  \sin(2x)  =  \frac{2 \tan(x) }{1 +  {( \tan(x)) }^{2} }  \\ then \\  \sin(2x)  +  \tan(2x)  =  \frac{2 \tan(x) }{1 -  {( \tan(x)) }^{2} }  +  \frac{2 \tan(x) }{1 +  {( \tan(x)) }^{2} }  \\  =  \frac{2 \tan(x)(1 +  {( \tan(x)) }^{2}  + 2 \tan(x) (1 -  {( \tan(x)) }^{2}  }{(1 +  {( \ \tan(x))  }^{2}(1 -  {( \tan(x)) }^{2}  }  \\  =  \frac{2 \tan(x) \times 2 }{1 -  {( \tan(x) }^{4} }  \\  =  \frac{4 \tan(x) }{1 -  {( \tan( \times ) )}^{4} }

Step-by-step explanation:

If you need any explanation. I can do it, my friend. you can communicate with me to that or any thing do you need in math

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8 0
3 years ago
Spencer wrote the following paragraph proof showing that rectangles are parallelograms with congruent diagonals. Quadrilateral R
Komok [63]

We have to prove that rectangles are parallelograms with congruent Diagonals.

Solution:

1. ∠R=∠E=∠C=∠T=90°

2. ER= CT, EC ║RT

3.  Diagonals E T and C R are drawn.

4. Shows Quadrilateral R E CT is a Rectangle.→→[Because if in a Quadrilateral One pair of Opposite sides are equal and parallel and each of the interior angle is right angle than it is a Rectangle.]

5.  Quadrilateral RECT is a Parallelogram.→→[If in a Quadrilateral one pair of opposite sides are equal and parallel then it is a Parallelogram]

6. In Δ ERT and Δ CTR

(a) ER= CT→→[Opposite sides of parallelogram]

(b) ∠R + ∠T= 90° + 90°=180°→→→Because RECT is a rectangle, so ∠R=∠T=90°]

(c) Side TR is Common.

So, Δ ERT ≅ Δ CTR→→[SAS]

Diagonal ET= Diagonal CR →→→[CPCTC]

In step 6, while proving Δ E RT ≅ Δ CTR, we have used

(b) ∠R + ∠T= 90° + 90°=180°→→→Because RECT is a rectangle, so ∠R=∠T=90°]

Here we have used ,Option (D) : Same-Side Interior Angles Theorem, which states that Sum of interior angles on same side of Transversal is supplementary.

6 0
3 years ago
Read 2 more answers
if you help me with this and get it right i’ll create another question for you to answer that’s free 20 points! just want to mak
gladu [14]

Answer:

Right so SAS means side angle side and the alternate angle theory is that any opposite angle is equal and the sides on the shape are parallel and to be honest thats all i know hope it kind of elps

Step-by-step explanation:

6 0
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Mnenie [13.5K]

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2 years ago
How do you solve X/2-5=10
Afina-wow [57]

Answer: x2-5=10  

Two solutions were found :

                  x = ± √15 = ± 3.8730

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x2"   was replaced by   "x^2".  

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    x^2-5-(10)=0  

Step by step solution :

Step  1  :

Trying to factor as a Difference of Squares :

1.1      Factoring:  x2-15  

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 15 is not a square !!

Ruling : Binomial can not be factored as the difference of two perfect squares.

Equation at the end of step  1  :

 x2 - 15  = 0  

Step  2  :

Solving a Single Variable Equation :

2.1      Solve  :    x2-15 = 0  

Add  15  to both sides of the equation :  

                     x2 = 15

 

When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:  

                     x  =  ± √ 15  

The equation has two real solutions  

These solutions are  x = ± √15 = ± 3.8730  

 

Two solutions were found :

                  x = ± √15 = ± 3.8730

Step-by-step explanation:

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