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

Mathematics

1 answer:

Solnce55 [7]4 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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in a population distribution a score of x=28 corresponds to z=-1.00 and a score of x=34 what is the mean and standard deviation

irakobra [83]

$x=28\implies z=\dfrac{28-\mu}\sigma\implies \mu-\sigma=28$

$x=34\implies z=\dfrac{34-\mu}\sigma\implies \mu+\sigma z=34$

We need the exact value of $z$ to find a proper solution, but a general one can still be found. Subtracting the first equation from the second gives

$(\mu+\sigma z)-(\mu-\sigma)=34-28\implies (z+1)\sigma=6\implies \sigma=\dfrac6{z+1}$

Plug this into either equation and you get

$\mu-\dfrac6{z+1}=28\implies \mu=28+\dfrac6{z+1}$

(It's guaranteed that $z\neq-1$ in this case because that already corresponds to $x=28$ .)