By "which is an identity" they just mean "which trigonometric equation is true?"
What you have to do is take one of these and sort it out to an identity you know is true, or...
*FYI: You can always test identites like this:
Use the short angle of a 3-4-5 triangle, which would have these trig ratios:
sinx = 3/5 cscx = 5/3
cosx = 4/5 secx = 5/4
tanx = 4/3 cotx = 3/4
Then just plug them in and see if it works. If it doesn't, it can't be an identity!
Let's start with c, just because it seems obvious.
The Pythagorean identity states that sin²x + cos²x = 1, so this same statement with a minus is obviously not true.
Next would be d. csc²x + cot²x = 1 is not true because of a similar Pythagorean identity 1 + cot²x = csc²x. (if you need help remembering these identites, do yourslef a favor and search up the Magic Hexagon.)
Next is b. Here we have (cscx + cotx)² = 1. Let's take the square root of each side...cscx + cotx = 1. Now you should be able to see why this can't work as a Pythagorean Identity. There's always that test we can do for verification...5/3 + 3/4 ≠ 1, nor is (5/3 + 3/4)².
By process of elimination, a must be true. You can test w/ our example ratios:
sin²xsec²x+1 = tan²xcsc²x
(3/5)²(5/4)²+1 = (4/5)²(5/3)²
(9/25)(25/16)+1 = (16/25)(25/9)
(225/400)+1 = (400/225)
(9/16)+1 = (16/9)
(81/144)+1 = (256/144)
(81/144)+(144/144) = (256/144)
(256/144) = (256/144)
Step-by-step explanation:
Remember:
SOH - Sin(angle) = Opposite/Hypotenuse
CAH - Cos(angle) = Adjacent/Hypotenuse
TOA - Tan(angle) = Opposite/Adjacent
Answer:
B
Step-by-step explanation:
Variance can be said to be a measure of dispersion for a random sample.
Variance = pq/n
When given the variance, we can find the standard deviation.
Standard deviation = √variance
= √pq/n
Answer:
The answer is
<h2>1225</h2>
Step-by-step explanation:
4x² + 5 - 6x³ + 3x⁴ - x
x = - 4
Substitute the value of x into the expression
That's
4(-4)² + 5 - 6(-4)³ + 3( 4 )⁴ - - 4
Simplify
4(16) + 5 - 6( -64) + 3( 256) + 4
64 + 5 + 384 + 768 + 4
We have the final answer as
<h3>1225</h3>
Hope this helps you
Rewrite the fraction as division:
Make them into single fraction:
Change the divide fraction into multiplication fraction:
Factorise the difference of square a² - b² = (a + b) (a - b) :
Cancel the common factors:
