Prove :
(tan x – cosec x )^2 – ( cot x – sec x)^2 = 2(cosec x – sec x)
LHS
= tan² x - 2 tan x cosec x + cosec² x - cot² x + 2 cot x sec x - sec² x
= tan² x - 2 sec x + cosec² x - cot² x + 2 cosec x - sec² x
= ( tan² x - sec² x ) + (cosec² x - cot² x) + 2 cosec x - 2 sec x
= -1 + 1 + 2 cosec x - 2 sec x
= 2 (cosec x - sec x)
= RHS (proved)
LHS:
= [(sin x /cos x) – (1/sinx)]^2 – [(cos x/sinx – 1/cosx)^2
= [(sin ^2 x – cos x)/(cos x sin x)]^2 – [(cos^2 x – sin x)/(cos x sin x)]^2
= [(sin ^2 x – cos x)/(cos x sin x)+ (cos^2 x – sin x)/(cos x sin x)] [(sin ^2 x – cos x)/(cos x sin x)– (cos^2 x – sin x)/(cos x sin x)]
= stucked…
RHS:
= 2[(cos x – sin x) / (sin x cos x)]
= Stucked…
... so ... S.O.S?
Originally posted by eagle:LHS
= tan² x - 2 tan x cosec x + cosec² x - cot² x + 2 cot x sec x - sec² x
= tan² x - 2 sec x + cosec² x - cot² x + 2 cosec x - sec² x
= ( tan² x - sec² x ) + (cosec² x - cot² x) + 2 cosec x - 2 sec x
= -1 + 1 + 2 cosec x - 2 sec x
= 2 (cosec x - sec x)
= RHS (proved)
o.O
thx ^^
but y cannot use a^2 - b^2?
Originally posted by tr@nsp0rt_F3V3R:o.O
thx ^^
but y cannot use a^2 - b^2?
err.... use for what?
Originally posted by eagle:err.... use for what?
(tan x – cosec x )^2 – ( cot x – sec x)^2
a= tan x – cosec x
b = cot x – sec x
merge = a^2 - b^2
can? or redundant?
it might be tougher and more troublesome to do it that way
the easiest method (usually) is to expand, then simplify
Originally posted by eagle:it might be tougher and more troublesome to do it that way
the easiest method (usually) is to expand, then simplify
o.O
thx alot ^^
tmr Trigo test.. now doing Shinglee tb... xian...
Try a few more questions here?
http://examworld.blogspot.com/search/label/O%20lvl%20AM%3A%20Trigonometric%20Identity
P.S. Updated your question inside as well :D
Originally posted by eagle:Try a few more questions here?
http://examworld.blogspot.com/search/label/O%20lvl%20AM%3A%20Trigonometric%20Identity
P.S. Updated your question inside as well :D
haha.. thx ^^
btw i'm using panpac TB and using Shinglee as resource...
Now quite busy doing till @.@ le + now i oso v. tired le...
so maybe try some qn l8r... sry ^^
now gonna hug my pillow le... ...
haha... nites ^^
thx btw ^^