25 ≡ x mod 5 not sure how to solve this pls

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

2 years ago

if a dog food costs 0.75 per pound, and dog bones cost 1.75 each, what is the cost of 2 bones and 25 pounds of dog food?

Studentka2010 [4]

Answer:

2 bones and 25 pounds of dog food would cost $22.25

Step-by-step explanation:

5 0

3 years ago

2). You are to construct the walls for the storage building that will be 8' high; using the

yulyashka [42]

Answer:28

Step-by-step explanation:

7 0

2 years ago

A Pizzeria sells pizza according to size: small pizzas cost $10, medium pizzas cost $15, and large pizzas cost $40. They usually

Kamila [148]

Answer:

a pizzeria sells three sizes of pizza: small, medium, and large. the pizzas sell for $9, $10, and $13, respectively.

one evening they sold 21 pizzas and received $220. if they sold 1 more medium than large pizzas, how many of each size did they sell?

Step-by-step explanation:

8 0

3 years ago

In the diagram what is the angle of depression?

Jlenok [28]

Answer:

$\angle EGD$

Step-by-step explanation:

Imagine that the point E is variable along the ED line.

As you lower E along ED, the angle EDG gets smaller and smaller, so this is the angle of depression.

3 0

2 years ago