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2 years ago

Simplify (1 − cos x)(1 + cos x). (2 points)

Mathematics

2 answers:

Vadim26 [7]2 years ago

4 0

Answer:

sin²x

Step-by-step explanation:

we have

(1 − cos x)(1 + cos x)=1-cos²x

Remember that

sin²x+cos²x=1 ------> i-cos²x=sin²x

therefore

(1 − cos x)(1 + cos x)=sin²x

liq [111]2 years ago

4 0

Answer:

$sin^2x$

Step-by-step explanation:

Given expression,

$(1 - cos x)(1 + cos x)$

By using $a^2-b^2=(a+b)(a-b)$

$(1 - cos x)(1 + cos x)=1^2 - cos^2x = 1 - cos^2x$

$\because sin^2x+cos^2x=1$

$\implies (1 - cos x)(1 + cos x)=sin^2x+cos^2x - cos^2x=sin^2x$

Since, further simplification is not possible,

Hence, the simplified form of the given expression is $sin^2x$

You might be interested in

What are the exact solutions of x2 − 5x − 7 = 0, where x equals negative b plus or minus the square root of b squared minus 4 ti

Marat540 [252]

Answer:

$x = \frac{5 + \sqrt{53}}{2}$ or $x = \frac{5 - \sqrt{53}}{2}$

Step-by-step explanation:

Given

$x^2 - 5x - 7 = 0$

Required

Solve for x using:

$x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}$

First, we need to identify a, b and c

The general form of a quadratic equation is:

$ax^2 + bx + c = 0$

So, by comparison with $x^2 - 5x - 7 = 0$

$a = 1$ $b = -5$ $c = -7$

Substitute these values of a, b and c in

$x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}$

$x = \frac{-(-5) \± \sqrt{(-5)^2 - 4 * 1 * -7}}{2 * 1}$

$x = \frac{5 \± \sqrt{25 +28}}{2}$

$x = \frac{5 \± \sqrt{53}}{2}$

Split the expression to two

$x = \frac{5 + \sqrt{53}}{2}$ or $x = \frac{5 - \sqrt{53}}{2}$

To solve further in decimal form, we have

$x = \frac{5 + 7.28}{2}$ or $x = \frac{5 - 7.28}{2}$

$x = \frac{12.28}{2}$ or $x = \frac{-2.28}{2}$

$x = 6.14$ or $x = -1.14$

4 0

2 years ago

Prinicipal Ramirez wants each of the 588 students at her school to solve 40 math problems for homework tonight. If every student

masha68 [24]

Step-by-step explanation:

588 × 40 = 23,520 math problems they would solve that evening

3 0

2 years ago

1. On her birthday, Shruti bought 2 kg sweets and distributed 1 kg 500 g among her classmates. How much sweets were left with he

uysha [10]

Answer:

500g

Step-by-step explanation:

since she brought 2 kg of sweets, and distributed to her classmates, that means we wil sustract 2 from 1,5 and that will be 0.5 or 500g

I hope I helped you! :)))

7 0

1 year ago

Read 2 more answers

Mops

Ipatiy [6.2K]

Answer:

270

Step-by-step explanation:

For any arithmetic sequence

nth term is given by

nth term = a + (n-1)d

where a is first term,

d is common difference

d is given by nth term - (n-1)th term

sum of n terms given by

sum = n/2(2a + (n-1)d)

________________________________________________

Given arithmetic sequence

-2,0,2,4,6,8...

first term a = -2

lets take third term as nth term and second term as (n-1)th term to find common difference d.

d = 2 - 0 = 2

using a = -2 , d = 2, n = 18

thus, sum of first 18 terms = n/2(2a + (n-1)d)

=18/2( 2*(-2) + (18-1) 2)

=9 ( -4 + 34)

=9 ( 30) = 270

Thus, sum of first 18 terms is 270.

7 0

2 years ago

Write the equation <br> it passes through (-5,-7) and (-5,7)

timurjin [86]

Answer:

x = -5

Step-by-step explanation:

Find the gradient:

m = change in y ÷ change in x
m = (7 - -7) ÷ (-5 - -5)
m = 14 ÷ 0
m = 0 - There is no gradient, and it is a vertical line

The equation is x = -5, because in both co-ordinate pairs, the x is -5 - only the y changes

Hope this helps!

3 0

2 years ago