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3 years ago

Verify the trigonometric identity. convert the left side of the relationship to look like the right side.

Mathematics

1 answer:

Tomtit [17]3 years ago

5 0

Answer:

Verified

Step-by-step explanation:

Use $\tan{x}=\frac{\sin{x}}{\cos{x}}$ , $\sin^2{x}+\cos^2{x}=1$ and $\sec{x}=\frac{1}{\cos{x}}$

LHS= $\tan^2{x}+1=\frac{\sin^2{x}}{\cos^2{x}} + 1=\frac{\sin^2{x}+\cos^2{x}}{\cos^2{x}}=\frac{1}{\cos^2{x}}=\sec^2{x}$ =RHS

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Evan went to the park and saw four animals.

dsp73

Answer:

He saw 1 duck and 3 dogs.

Step-by-step explanation:

Given:

Evan went to the park and saw four animals.

Each animal was either a duck or a dog.

He saw a total of 14 legs.

Now, to find the number of each animal he had seen.

Let the number of duck be $x.$

And the number of dog be $y.$

So, total number of animals:

$x+y=4\\y=4-x$

Now, the total number of legs he did see:

As we know the legs of a duck are 2 and a dog are 4.

$2x+4y=14\\2x+4(4-x)=14\\2x+16-4x=14\\-2x+16=14$

Adding both sides by -16 we get:

$-2x=-2$

Dividing both sides by -2 we get:

$x=1$

The number of duck = 1.

Now, putting the value of $x$ in above equation we get:

$y=4-x$

$y=4-1\\y=3.$

The number of dogs = 3.

Therefore, he saw 1 duck and 3 dogs.

4 0

3 years ago

In the figure, angle D measures 45° and angle E measures 87°. What is the measurement of angle H? 42°

Vinvika [58]

The complete question is shown in the attached image

Answer:
measure angle H = 42°

Explanation:
There is a theorem that states that:
"In a triangle, the measure of the exterior angle is equal to the sum of the measures of the two non-adjacent angles to the exterior angle"

In the given, we have:
angle E is an exterior angle to triangle DFH
The two non-adjacent angles to angle E are angles D and H

Based on the above rule:
measure angle E = measure angle D + measure angle H

We are given that:
angle E = 87°
angle D = 45°

Substitute with the givens in the above rule and solve for the measure of angle H as follows:
angle E = angle D + angle H
87° = 45° + measure angle H
measure angle H = 87° - 45°
measure angle H = 42°

Hope this helps :)

3 0

3 years ago

The point ( -6 , 8 ) is reflected across the y axis. What is the coordinates of the reflection

Digiron [165]

The new coordinations would be (6,8)

6 0

3 years ago

Read 2 more answers

A(n)=-6-4(n-1) Find the 4th term in the sequence

Soloha48 [4]

All we have to do is replace n with 4.
-6-4(4-1)
Parenthesis first.
-6-4×3
Multiplication next.
-6-12
Now subtract.
-18
The 4th term is -18.
Tell me if this helps!!

8 0

3 years ago

Read 2 more answers

I need help with both, please explain thoroughly. Does it make a difference if it says "from the origin" or "about vertex _"???

Vitek1552 [10]

Answer:

Yes

Step-by-step explanation:

From the origin means from the centre or middle but about a vertex is from a named point.

7 0

3 years ago