Question

Prove the following identities:
Can anyone can help me here..i will give medals and i will be your fan

Answer 1

\[\frac{ \sin +\tan }{ \cot + \csc }=\sin \tan \]

Answer 2

@cwrw238

Answer 3

@TheSmartOne

Answer 4

this is a tricky one - i'll have a look at it now

Answer 5

ok... i have 3 more identities here
if you dont mind can we solve that all?

Answer 6

I can solve this one - first convert everything to sin's and cos's

- i'll write s for sin and c for cos

Answer 7

left side = (s + s/c )/ (cs + 1/s0
right side = s * (s/c)

so lets try and simplify the left side and get the right

Answer 8

ok

Answer 9

= sc + s c + 1 s(sc + s)
----- / ---- = -------
c s c^2 + c

Answer 10

is it possible that we convert the 2 sides? or can we solve first in one side?

Answer 11

= s^2c + s^2 s^2(c + 1)
--------- = -------- = s^2 / c = right side
c^2 + c c(c + 10

Answer 12

so its just algebra

Answer 13

- wher you see 10 its a typo - should be 1)

Answer 14

i've used the identities tan = sin/cos , cot = cos/sin and csc = 1/sin

Answer 15

check out my third post - more typos
it should read
left side = (s + c/s) / ( c/s + 1/s)

Answer 16

- because tan = s/c , cot = c/s and csc = 1/s

Answer 17

shoot - whats wrong with me
that (c + s/c) in the first bracket!!!

Answer 18

how did you derive s(sc+s)/c^2+cos to sin^2/cos

Answer 19

in the right side

Answer 20

ok - first expand the top part
= s^2 c + s^2


and bottom part is c^2 + c

to give s^2 c + s^2
---------
c^2 + c

now factor top and bottom

s^2( c + 1)
---------
c(c + 1)

the (c +1) will cancel out to give

s^2/c which is the right hand side

Answer 21

when you have a mix of sec, cots tans or whatever its often best to convert to sines and cosines
then aim to convert the more complicated side to get the simpler one

Answer 22

do you follow it ok?

Answer 23

its a bit long winded i know - there might be a shorter way to do it but i cant think of one.

Answer 24

ok ok i get it

Answer 25

can we solve another?

Answer 26

well i 've got 10 minutes only i'm afraid but ok

Answer 27

1-2c^2/sc = tans-cot

Answer 28

can we prove only the left side?

Answer 29

well we need to convert one side to the other

Answer 30

ok

Answer 31

can you post it all at once :D

Answer 32

RHS = s/c - c/s = s^2 - c^2 / sc = cos2x / sinx cos x

Answer 33

sorry I cant at the moment because the 'post' box is running off the screen so i cant click on it

Answer 34

LHS = cos 2x / sc
so both sides are the same

Answer 35

I've used the 2 identities
sin^2 x - cos^2 x = cos2x and 1 - 2cos^2 x = cos 2x

Answer 36

gotta go right now