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hello everyone i can't seem to figure these few out....
solve these using fundamental identites...
here is an example of one i did...
u can use either side to start solving so it matches the opposite side.
sin^2x(1 + cot^2x) = 1
sin^2+sin^2xcot^2x
sin^2x + sinx cos^2x/sin^2x <---sin's cross out
sin^2x + cos^2x = 1 <----so there u go
1. cotx + tanx = secx cscx
2. sin^2x + tan^2 x + cos^2x = sec^2x
thanks all, later!
Well, as no one else has answered your question, I'll give it a go...
1) cotx + tanx = secx cscx
[I'm afraid I don't know what cscx is. Do you mean cosecx?]
[If you do, reply to the post ajd I'll show you how it's done]
[If it's not supposed to be cosecx and it is cscx, i'm afraid I ]
[don't know how to solve it! ]
2) sin^2x + tan^2 x + cos^2x = sec^2x
[Use the rule: sec^2 = 1 + tan^2x] So...
sin^2x + tan^2 x + cos^2x = 1 + tan^2x
[Take tan^2x from both sides] So...
sin^2x + cos^2x = 1 <----so there u go!!
If you need any more help on this just reply to the post.
------------------
Lloyd Morgan
UK
hey thanks for ur reply but i don't think thats right, see what ur trying to do is make the 2 sides == to eachother, such as
if you have sin^2x+tan^2x + cos^2x = sec^2x
u can either start on teh left side and make it equal the right side or vice versa...
so say u start with the left side, u only have
sin^2x + tan^2x + cos^2x to work with, u must make that some how equal the right side
and yes
csc == cosine
sin == sine
sec == secant
cos == cosecant
tan == tangent
cot == cotangent
i think i figured out the one u tried but i still can't figure out the top one, the answer to
sin^2x + tan^2x + cos^2x = sec^2x
since sin^2x + cos^2x = 1 u can put
1 + tan^2x = sec^2x
and since 1 + tan^2x == sec^2x, ur done!
Ah, yes, I'm afraid I only realised that also about an hour after I posted it.
I should have known that anyway, because I got set a load of questions to do only last week on this exact topic for A-level maths.
About the other question:
cotx + tanx = secx cosecx
At last I can be some use, as we got given this exact question last week and I got it right! Here it is... copying right off my paper:
cotx + tanx = secx cosecx
[tanx = sinx / cosx] Therefore
[as cotx = 1 / tanx ... cotx = cosx / sinx] So...
(cosx / sinx) + (sinx / cosx) = secx cosecx
[Make a common denominator & sort it out] So...
(cos^2x + sin^2x) / cosx sinx = secx cosecx
[cos^2x + sin^2x = 1] So...
1 / cosx sinx = secx cosecx
(1 / cosx) (1 / sinx) = secx cosecx
[(1 / cosx = secx) & (1 / sinx = cosecx)] So...
secx cosecx = secx cosecx
-------------------
Is this OK now? I hope so.
Regards,
Lloyd
excellent job, works great