-10.7 as a mixed number in simplest form

Futhe Mathematics <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 :-

Derivation of cos²x - sin²x = cos2x :-

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

3 years ago

Find the midpoint of the segment with the following endpoints. (10, 7) and (5, 4)

KatRina [158]

Answer:

$\frac{15}{2} , \frac{11}{2}$

Step-by-step explanation:-

To find the midpoint, the equation we use is:-

$\frac{x1 +x2}{2} , \frac{y1 + y2}{2}$

x1 = 10

x2 = 5

y1 = 7

y2 = 4

Substituting the values in the equation, we get:-

$\frac{10+5}{2} , \frac{7+4}{2}$

Coordinates of the midpoint---> $\frac{15}{2} , \frac{11}{2}$

8 0

3 years ago

Choose the missing step in the given solution to the inequality −x − 10 > 14 + 2x. −x − 10 > 14 + 2x −3x − 10 > 14 ____

Tresset [83]

Answer:

−3x > 24

Step-by-step explanation:

Adding 10 to both sides of the inequality will give the missing step:

-3x -10 +10 > 14 +10

-3x > 24

8 0

3 years ago

Read 2 more answers

A family wants to remodel a house and spend at most $135,000 total for the entire project. a)If the builder wants to make a 15%

Troyanec [42]

Jjjbbjujbujbb. In un cmk bye j Sheeeeeeeesh

3 0

3 years ago

Ordered pairs that is satisfy to the equation y=-9x+3

trasher [3.6K]

Let x = 1. Substitute x = 1 into the equation:

y = -9X(1)+3

y = -9+3

y = -6

-> Ordered pairs are written in the form (x,y). Thus in this case, your ordered pair is (1,-6).

4 0

3 years ago