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urgent:trigonometric equation help and a few other questions

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lhl_anecar:
Can someone please kindly help me solve these questions

1. state the standard identity relating cos and sin arising from Pythagoras Theorem
    sec^2(x) + cosec^2(x) = sec^2(x) x cosec^2(x)

I have no idea what the question wants.

and this question

2. ln x + ln(1-x)-2ln(1+x)

It looks so simple but i just cant seem to get it right.. help :(
 
3. 5 x (1.5)^a = 100

how do i get a?

4. find the deriavative of the following

a) y=x^5e^x + 3xlnx

b. R=(e^t+1)(t-ln t)

y=(x^5)(e^x) + 3xlnx    how do i solve this??

Freaked12:
what do you have to do
 simplify ?
 or equate ?

if we simplify
its coming
 ln[ (x-x*) / (1+x)* ]
 x* means x squared

and if we equate

 then you remove the ln
 by making the other side the power of e
 and equation it to the thing iside the ln bracket
 that will make a quadratic equation in x

Freaked12:
just remember
if lnx - lnx
then its equal to ln [ x/x ]
and if lnx + lnx then it equals ln [x multiplied by x ]

ashish:

--- Quote from: lhl_anecar on October 16, 2010, 06:26:18 pm ---Can someone please kindly help me solve these questions

1. state the standard identity relating cos and sin arising from Pythagoras Theorem
    sec^2(x) + cosec^2(x) = sec^2(x) x cosec^2(x)

I have no idea what the question wants.



--- End quote ---

the equation is
cosx2 + sinx2 = 1

for the second one i have to prove ?

secx is 1/cosx  and cosecx is 1/sinx

from left hand side

sec2x + cosec2x = 1/cos2x + 1/sin2x
         expressing as a single fraction
 
                                                      =(sin2x + cos2x)/ cos2x sin2x
                                                       = 1/sin2x   *   1/cos2x

                                                        = cosec2x  *  sec2x

ashish:

--- Quote from: lhl_anecar on October 16, 2010, 06:26:18 pm ---Can someone please kindly help me solve these questions



It looks so simple but i just cant seem to get it right.. help :(
 
3. 5 x (1.5)^a = 100

how do i get a?



--- End quote ---

3.5 * (1.5)a =100
          1.5a= 100/3.5
         taking ln on both side
         ln1.5a= ln(100/3.5)
                  power becomes multiplier (one property of log)
                  a=(ln(100/3.5))/ln1.5
                   a =8.268

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