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2 years ago

15

Factorise completely: 12a+8b

1 answer:

zavuch27 [327]2 years ago

6 0

12a + 8b....common factor is 4
4(3a + 2b) <==

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Futhe Mathematics<br><img src="https://tex.z-dn.net/?f=%28Cos%20%7B%7D%5E%7B4%7Dt%20-Sin%20%7B%7D%5E%7B4%7Dt%20%29%20%20%5Cdiv%2

Nastasia [14]

Answer:

cos2t/cos²t

Step-by-step explanation:

Here the given trigonometric expression to us is ,

$\longrightarrow \dfrac{cos^4t - sin^4t }{cos^2t }$

We can write the numerator as ,

$\longrightarrow \dfrac{ (cos^2t)^2-(sin^2t)^2}{cos^2t }$

Recall the identity ,

$\longrightarrow (a-b)(a+b)=a^2-b^2$

Using this we have ,

$\longrightarrow \dfrac{(cos^2t + sin^2t)(cos^2t-sin^2t)}{cos^2t}$

Again , as we know that ,

$\longrightarrow sin^2\phi + cos^2\phi = 1$

Therefore we can rewrite it as ,

$\longrightarrow \dfrac{1(cos^2t - sin^2t)}{cos^2t}$

Again using the first identity mentioned above ,

$\longrightarrow \underline{\underline{\dfrac{(cost + sint )(cost - sint)}{cos^2t}}}$

Or else we can also write it using ,

$\longrightarrow cos2\phi = cos^2\phi - sin^2\phi$

Therefore ,

$\longrightarrow \underline{\underline{\dfrac{cos2t}{cos^2t}}}$

And we are done !

$\rule{200}{4}$

Additional info :-

<em>D</em><em>e</em><em>r</em><em>i</em><em>v</em><em>a</em><em>t</em><em>i</em><em>o</em><em>n</em><em> </em><em>o</em><em>f</em><em> </em><em>c</em><em>o</em><em>s</em><em>²</em><em>x</em><em> </em><em>-</em><em> </em><em>s</em><em>i</em><em>n</em><em>²</em><em>x</em><em> </em><em>=</em><em> </em><em>c</em><em>o</em><em>s</em><em>2</em><em>x</em><em> </em><em>:</em><em>-</em>

We can rewrite cos 2x as ,

$\longrightarrow cos(x + x )$

As we know that ,

$\longrightarrow cos(y + z )= cosy.cosz - siny.sinz$

So that ,

$\longrightarrow cos(x+x) = cos(x).cos(x) - sin(x)sin(x)$

On simplifying,

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

Hence,

$\longrightarrow\underline{\underline{cos (2x) = cos^2x - sin^2x }}$

$\rule{200}{4}$

7 0

2 years ago

Joe’s balance in his checking account at the beginning of the month was $132. At the end of the month, it was 15.3% higher. What

Contact [7]

The answer would be $152.20 because 132*1.153=152.196, rounded to $152.20.

4 0

2 years ago

Six plus four fifths A equals nine tenths A

Drupady [299]

6+4/5a=9/10a
make bottom numbers same
into 10
60/10+8/10a=9/10a
minus 8/10a from both sides
60/10=1/10a
multiply both sides by 10
60=a

8 0

2 years ago

Ashley is choosing a popsicle from the freezer at random the probability of her picking a grape popsicle is 3/8 the probability

netineya [11]

If an experiment has $N$ possible outputs, each with probability

$P_1,\ P_2,\ldots,\ P_N$

then the sum of all probabilities is always one:

$P_1 + P_2 + \ldots + P_N=1$

So, in your case, you have

$P(\text{grape}) + P(\text{cherry}) + P(\text{orange}) = 1$

plugging in the given values:

$\dfrac{3}{8} + \dfrac{1}{3} + P(\text{orange}) = 1 \iff \dfrac{17}{24} + P(\text{orange}) = 1$

we can deduce that

$P(\text{orange}) = 1-\dfrac{17}{24} = \dfrac{7}{24}$

8 0

3 years ago

GIVING BRAINLIEST ONLY IF 100% CORRECT-NO GUESSES NO LINKS

vovangra [49]

Answer:

b, c, and d

Step-by-step explanation:

b and c are rhombuses and d is a trapezoid. rhombuses are not rectangles, nor are trapezoids.

7 0

3 years ago