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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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2 years ago

A man can drive a motorboat 70 miles down the Colorado River in the same amount of time that he can drive 40 miles upstream. Fin

pochemuha

The speed of the current is 40.34 mph approximately.

SOLUTION:

Given, a man can drive a motorboat 70 miles down the Colorado River in the same amount of time that he can drive 40 miles upstream.

We have to find the speed of the current if the speed of the boat is 11 mph in still water. Now, let the speed of river be a mph. Then, speed of boat in upstream will be a-11 mph and speed in downstream will be a+11 mph.

And, we know that, $\text{ distance } =\text{ speed }\times \text{ time }$

$\begin{array}{l}{\text { So, for upstream } \rightarrow 40=(a-11) \times \text { time taken } \rightarrow \text { time taken }=\frac{40}{a-11}} \\\\ {\text { And for downstream } \rightarrow 70=(a+11) \times \text { time taken } \rightarrow \text { time taken }=\frac{70}{a+11}}\end{array}$

We are given that, time taken for both are same. So $\frac{40}{a-11}=\frac{70}{a+11}$

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3 years ago

Solve for x. 50 = x^2 Show your work.

Tanzania [10]

50 = x^2

To isolate x you need to do the opposite of an exponent, which would be square root.

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7.07 = x

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3 years ago

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vova2212 [387]

Answer:

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Step-by-step explanation:

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2 years ago

12-2(n-1)=-18 aa help plzz

Luda [366]

Answer:

n=16

Step-by-step explanation:

Let's solve your equation step-by-step.

12−2(n−1)=−18

Step 1: Simplify both sides of the equation.

12−2(n−1)=−18

12+(−2)(n)+(−2)(−1)=−18(Distribute)

12+−2n+2=−18

(−2n)+(12+2)=−18(Combine Like Terms)

−2n+14=−18

Step 2: Subtract 14 from both sides.

−2n+14−14=−18−14

−2n=−32

Step 3: Divide both sides by -2.

−2n /−2 = −32 /−2

n=16

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3 years ago