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Help! How would I solve this trig identity?

NeTakaya

Using simpler trigonometric identities, the given identity was proven below.

<h3>How to solve the trigonometric identity?</h3>

Remember that:

$sec(x) = \frac{1}{cos(x)} \\\\tan(x) = \frac{sin(x)}{cos(x)}$

Then the identity can be rewritten as:

$sec^4(x) - sen^2(x) = tan^4(x) + tan^2(x)\\\\\frac{1}{cos^4(x)} - \frac{1}{cos^2(x)} = \frac{sin^4(x)}{cos^4(x)} + \frac{sin^2(x)}{cos^2(x)} \\\\$

Now we can multiply both sides by cos⁴(x) to get:

$\frac{1}{cos^4(x)} - \frac{1}{cos^2(x)} = \frac{sin^4(x)}{cos^4(x)} + \frac{sin^2(x)}{cos^2(x)} \\\\\\\\cos^4(x)*(\frac{1}{cos^4(x)} - \frac{1}{cos^2(x)}) = cos^4(x)*( \frac{sin^4(x)}{cos^4(x)} + \frac{sin^2(x)}{cos^2(x)})\\\\1 - cos^2(x) = sin^4(x) + cos^2(x)*sin^2(x)\\\\1 - cos^2(x) = sin^2(x)*sin^2(x) + cos^2(x)*sin^2(x)$

Now we can use the identity:

sin²(x) + cos²(x) = 1

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

Thus, the identity was proven.

If you want to learn more about trigonometric identities:

brainly.com/question/7331447

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7 0

1 year ago

What is the domain of the following graph? Please don't put links down I cant download them.

rosijanka [135]

Answer:

-infinity, infinity

Step-by-step explanation:

Domain is x, and in a quadratic equation like this one the x axis goes on forever. So the first answer of -infinity, infinity is correct.

8 0

3 years ago

Read 2 more answers

Geometry help! this is my 2nd to last question

Kryger [21]

A square since all sides are equal and the angles aren't acute so it can't be a rhombus

7 0

3 years ago

Read 2 more answers

Lorraine is picking blackberries in her backyard at a rate of 15 berries per minute. After 16 minutes of picking, there are stil

lyudmila [28]

137 - 16X = Y

Since Lorraine is picking blackberries in her backyard at a rate of 15 berries per minute, and after 16 minutes of picking, there are still 137 blackberries left to pick, to determine an equation that models how many berries are left (y) after x minutes of picking, the following calculation must be performed:

137 - 16X = Y

Thus, for example, after 5 minutes the calculation would be as follows:

137 - 16 x 5 = Y
137 - 80 = Y
57 = Y

Learn more about maths in brainly.com/question/25989509

8 0

2 years ago

A car rental company rents cars for x dollars per day plus y dollars for each mile driven. Carlos rented a car for 4 days, drove

topjm [15]

Answer:

x = $20/day, y = $0.35/mile

Step-by-step explanation:

x = $/day, y = $/mile

4x + 160y = 136

1x + 240y = 104

You can solve by elimination or substitution.

4 0

2 years ago