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3 years ago

Consider the line 9X - 8Y = 6

Mathematics

1 answer:

kenny6666 [7]3 years ago

8 0

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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

Two complementary angles are such that one is 15 degrees less than

Softa [21]

Answer:

35 and 55

Step-by-step explanation:

x+(2×-15)=90

3x-15=90

3x=105

x=35

other angle is 35×2-15=55

4 0

2 years ago

Read 2 more answers

Solve the radical equation. which is an extraneous solution to the radical equation? x = −1 x = 1 x = 5 there are no extraneous

qwelly [4]

Hence, the correct option is (D)There are no extraneous solutions to the equation.

<h2>What is an expression?</h2>

expression is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.). This math operation can be addition, subtraction, multiplication, or division. The structure of an expression is: Expression is (Number/Variable, Math Operator, Number/Variable)

<h3>How to solve?</h3>

the correct option is (D)There are no extraneous solutions to the equation.

to learn more about expressions: brainly.com/question/1859113

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8 0

1 year ago

You wish to make a triangular garden. One of the angles is 26°. The second angle is complementary to the first angle. What is th

rosijanka [135]

Since the second angle + first angle is 90 degrees, the third angle must be 90 degrees to complete the 180 degrees in a circle.
Hope this helps!

8 0

3 years ago

Please Help

artcher [175]

Multiply equation B by 2.
Multiply equation A by 2
Multiply equation B by 3.
Multiply equation A by -3

Answer: D

5 0

3 years ago