3 years ago

The equation tan^2 x+1=sec^2 x is an identity true or false

Mathematics

1 answer:

Solnce55 [7]3 years ago

8 0

Answer:

tan²x + 1 = sec²x is identity

Step-by-step explanation:

* Lets explain how to find this identity

∵ sin²x + cos²x = 1 ⇒ identity

- Divide both sides by cos²x

∵ sin x ÷ cos x = tan x

∴ sin²x ÷ cos²x = tan²x

- Lets find the second term

∵ cos²x ÷ cos²x = 1

- Remember that the inverse of cos x is sec x

∵ sec x = 1/cos x

∴ sec²x = 1/cos²x

- Lets write the equation

∴ tan²x + 1 = 1/cos²x

∵ 1/cos²x = sec²x

∴ than²x + 1 = sec²x

- So we use the first identity sin²x + cos²x = 1 to prove that

tan²x + 1 = sec²x

∴ tan²x + 1 = sec²x is identity

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3 years ago

On the following number line, two rational numbers are graphed.Represent the two numbers as fractions (or mixed numbers) in lowe

nordsb [41]

The first graphed rational number is at the middle of -2 and -1, thus the number represented is $-1 \frac{1}{2}$

The second graphed number is five out of six places from from 0 to 1, thus the number graphed is $0+ \frac{5}{6} = \frac{5}{6}$

The difference between the two numbers can be represented as
$-1 \frac{1}{2} - \frac{5}{6}$
or
$\frac{5}{6} -(-1 \frac{1}{2} )= \frac{5}{6} +1 \frac{1}{2}$

To find the difference,

$-1 \frac{1}{2} - \frac{5}{6} \\ \\ =-1 \frac{3+5}{6} \\ \\ =-1 \frac{8}{6} =-2 \frac{2}{6} \\ \\ =-2 \frac{1}{3}$

Also,

$\frac{5}{6} +1 \frac{1}{2} \\ \\ =1 \frac{5+3}{6} \\ \\ =1 \frac{8}{6} =2 \frac{2}{6} \\ \\ =2 \frac{1}{6}$