# math

i have a few questions

cosx + cosx =2secx
----- -----
1+sinx 1-sinx

cos(x-B)-cos(x-B) = 2sinxsinB

csc2x= 1 secx cscx
---
2

cotx= cos5x+cos3x
-----------
sin 5x-sin 3x

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1. for the first one:

LS = cosx/(1+sinx) + cosx/(1-sinx)

getting a common denominator of (1+sinx)(1-sinx)
= [cosx(1-sinx) + cosx(1+sinx)]/(1+sinx)(1-sinx)
= 2cosx/(1-sin^2)
= 2cosx/cos^2x
= 2/cosx
= 2secx
= RS

for cos(x-B)-cos(x-B) = 2sinxsinB

use the formula cos(A-B) = cosAcosB + sinAsinB on the Left Side, it comes apart very nicely after that

For the last two, try changing all trig ratios into sines and cosines.
Show me what you get

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2. for cos(x-B)-cos(x-B) = 2sinxsinB
you must have a typo, the LS is zero the way it stands
I am sure you meant

cos(x-B)-cos(x+B) = 2sinxsinB

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3. i don't understand how to use the formula in the second problem. what would i plug into A and B?

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4. cos(x-B)-cos(x+B) = 2sinxsinB

LS
= cosxcosB + sinxsinB - (cosxcosB - sinxsinB)
=2sinxsinB
= RS

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