School and Work: equations

cidyah has taken the correct approach. His answer is correct with one exception. Your solution set can only contain values of x for which the expression on the left and right are defined. The number p/2 is not in the domain of the expression on the right. It can not be included in the solution set.

sec(x) - tan(x) = cos(x)

1/cos(x) - sin(x)/cos(x) = cos(x) ==> 1 - sin(x) = cos²(x)

with the restriction that cos(x) ? 0. Use the ID cos²(x) = 1 - sin²(x):

1 - sin(x) = 1 - sin²(x) ==> sin²(x) - sin(x) = 0 ==> sin(x)[sin(x) - 1] = 0

So either sin(x) = 0, or 1 - sin(x) = 0.

sin(x) = 0 if x = 0, p, 2p, ..., kp where k is any integer.

sin(x) = 1 if x = p/2, 5p/2, ..., p/2 + 2pk for any integer k.

However, the latter values are not in the domain of either the secant or the tangent. So these are not in the solution set. The complete solution set can be expressed as

{x | x = kp, k any integer}.

**** Update ****

Beware! Every respondent that includes 90° or p/2 is in error!

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Open Question: What are the inonic and net ionic equations?

(use a table of solubility to determine which of the products [if any] will precipitate. The write an ionic and net ionic equation. )
H2O2 = H20 + O2
PtCl4 + Cl2 + PtCl6
NaC2H3O2 + H2SO4 = Na2SO4 + HC2H3O2
Pb(OH)2 + Hg2S = Pb@ + Hg2(OH)2

please help me with as many as you can :)
i know that i didnt balance the equations yet

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Open Question: college algebra= sustems of equations! help please im so concused!!?

1.at a school play 129 tickets were sold adult ticket cost 1.50 and childrens tickets cost 0.75 in all 153 was taken in how many of each kind of ticker were sold

2.a sporting goods store recevies a shipment of 124 golf bags the shipmetn includes two types of bags full size and collapisble the full size bags cost 38.50 the collapsible bags cost 22.50 each the bill fothe shope ment is 3430.00 how many of each type golf bags are in the shioment?

3. you and a friend share the driving on a 280 mile trip your average speed is 58 miles perhour you friends average speed i 53 miles per hour you drive one hour longer than your friend how many hours did eah of you drive?

4. flying with the wind a small plane flew 320 miles in 2 hours against the wind the plane could fly only 280 miles in the same amount of time find the rate of the plane in calm ari and the rate of the wind.

5. flying with the wind a pilot flew 450 miles between two cities in 2.5 hours the return rip against the wind took 3 hours find therate of the plane in calm air also fine the rate of the wind.

6. a store owener purchase twenty 60-watt- light bulbs and thirthy fluoresecent lights for a total cost of 40 a second purchase at the same prices included thirty 60-watt bulbs and ten fluorsecent lights for a total of 25. find the cost of a 60 watt bulb and a fluorsescent light.

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