Find x. Round your answer to the nearest tenth of a degree.<br> 36<br> X<br> 19<br> +

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

Mary and Julie both have a goal of raising $1000 for charity. Mary raises $12 every 4 days. Julie raises $19 every 6 days.

baherus [9]

Julie would reach her goal first. Julie would reach her goal in approximately 316 days while it would take Mary approximately 333 days to reach it.

I know this because the steps to solve the problem are:

1.) 1,000/12 = 83.333 (to find how many days it would take her everyday)

2.) 83.333x4 = 333 (multiplying the answer by four makes it every four days)

3.) determine that it takes Mary 333 days

4.) 1,000/19 = 52.631 (just like step 1 but with different numbers)

5.) 52.631x6 = 316 (just like in step 2 but different numbers)

6.) determine it takes Julie 316 days

7.) 316 < 333 (takes Julie less time)

6 0

3 years ago

Read 2 more answers

The longest side in a right triangle is 24 cm, and the second longest side is 20 cm. Find the length of the shortest side

harkovskaia [24]

Answer:

13.3 cm

Step-by-step explanation:

Apply the Pythagorean Theorem:

hyp² = (2nd longest side)² + (shortest side)². Here the numbers are:

(24 cm)² = (20 cm)² + (shortest side)², or

576 - 400 = 176 = hyp²