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Mamont248 [21]
3 years ago
6

Which of the following are identities? Check all that apply.

Mathematics
2 answers:
Genrish500 [490]3 years ago
7 0

Answer:

B and C and D

Step-by-step explanation:

This will help,

Ivenika [448]3 years ago
7 0

Answer:

Options A and D.

Step-by-step explanation:

To check the identities we have to check each option given.

A. tan(x - π) = tanx

We take left hand side (L.H.S.) of the equation.

tan(π - x) = tanx [ since we know tan(π ± x) = tanx ]

So L.H.S. = R.H.S.

It's an identity.

B. sin(x + y) + sin(x - y) = 2cosx siny

We take L.H.S. first

sin(x + y) + sin(x - y)

= sinx coxy + siny cosx + sinx cosy - cosx siny

= 2sinx cosy ≠ R.H.S.

Option B is not an identity.

C. cos(x + y) - cos(x - y) = 2cosx cosy

We take L.H.S. of the equation.

cos(x + y) - cos(x - y) = cosx cosy - sinx siny - (cosx cosy + sinx siny)

= -2sinx siny ≠ R.H.S.

Therefore, option C is not an identity.

D. cos(x + y) + cos(x - y) = 2cosx cosy

We take L.H.S. of the equation.

cos(x + y) + cos(x - y) = cosx cosy - sinx siny + cosx cosy + sinx siny

                                  = 2cosx cosy = R.H.S.

Therefore, option D is an identity.

Options A and D are the identities.

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Arada [10]

Answer:

[1]

Given: (5x^3 + 3x^2 - 7x + 10) - (3x^3 - x^2 + 4x - 1)

Remove the parenthesis, we get;

(5x^3 + 3x^2 - 7x + 10) - (3x^3-x^2+ 4x -1)

5x^3 + 3x^2 - 7x + 10- 3x^3 + x^2- 4x + 1

Like terms are the those terms with same variable and powers.

Combine like terms;

2x^3 + 4x^2 - 11x + 11

To write this polynomial in standard form, you write starting with the term with the highest degree, or exponent(i.e x^3), and then in decreasing order .

Standard form: 2x^3 + 4x^2 - 11x + 11

To, classify a polynomial by degree, you just look at the highest exponent, or degree.

Since, 3 is the highest degree (x^3), it is a cubic.

Now, classify a polynomial by the number of terms, count how many terms are in the polynomial( 2x^3 + 4x^2 - 11x + 11)

Number of terms: 4 (so this is polynomial)

[2]

Similarly,

for  (9w - 4w^2 + 10) + (8w^2 + 7 + 5w)

Remove the parenthesis, we get;

9w - 4w^2 + 10+ 8w^2 + 7 + 5w

Combine like terms; we have

14w + 4w^2 + 17

Standard form: 4w^2 + 14w + 17

Degree of the polynomial is, 2

Number of terms: 3 ( so, this is trinomial)



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