Trigonometric Identities (1 Viewer)

[Lukybear]

In 2 Unit HSC mathematics when proving trig identities. Do we ONLY prove one side to make it the same as the other. Or do we prove booth sides to a certain form?

Are there some questions in 2 UNIT math that require proving booth sides?

and also just as example how would you do this question? Is it possible to only prove LHS?

sin^2a . tana + cos^2a . cota + 2sina . cosa = tana + cota

sin^2a = (sina)^2

sorry for bad form.

 

[Drongoski]

In 2 Unit HSC mathematics when proving trig identities. Do we ONLY prove one side to make it the same as the other. Or do we prove booth sides to a certain form?

Are there some questions in 2 UNIT math that require proving booth sides?

and also just as example how would you do this question? Is it possible to only prove LHS?

sin^2a . tan^2a + cos^2a + 2sina . cosa = tana + cota

sorry for bad form.

In proving trig identities you can show:

LHS = .. = .. = . . . = RHS

RHS = .. = .. = . . . = LHS

LHS = .. = .. = . . = Intermediate Expression
RHS = .. = .. = . . = same Intermediate Expression


To me the 1st 2 are to be preferred; you usually go from the side that is more complex to the side that's simpler.

Usually students with poorer command of standard trig identities & algebraic fiddling tend to resort to the 3rd.

 

[Timothy.Siu]

dont think that question works

 

[Drongoski]

I too think a wrong 'identity' has been posted.

Didn't work for a = pi/6 and (I tried again) not for pi/3 either.

 

[Lukybear]

O yeas my mistake, so sorry. I ve changed the question. Its just basic proof of 2 unit.

 

[Timothy.Siu]

still dont think it works

 

[Lukybear]

Im sure it does. Ive done it, but i had to get LHS to one point. Then convert RHS as well. Its from 2 Unit Fitz, p174, q 18.

Just to make that notation clearier.
. = X
a= delta
^ power of

Hope it makes things clearier.

 

[Timothy.Siu]

yeah i was reading it wrong.

LHS=sin^3 a/cos a +cos^3 a/sin a + 2sin a cos a

=(sin^4 a+cos^4 a + 2sin^2 a cos^2 a)/cos a.sin a (putting all on same denominator)

=(sin^2 a+cos^2 a)^2/cos a. sin.a
(sin^2 a + cos^2 a=1)
=(sin^2 a+cos^2 a)/cosa.sina
=tan a+cot a=rhs

 

[Lukybear]

How does
(sin^2 a+cos^2 a)/cosa.sina = tan a + cot a
unless you put RHS = 1/ cosa.sina
and LHS = 1/cosa.sina

Or does the question allow you to infer?

 

[Timothy.Siu]

How does
(sin^2 a+cos^2 a)/cosa.sina = tan a + cot a
unless you put RHS = 1/ cosa.sina
and LHS = 1/cosa.sina

Or does the question allow you to infer?

(sin^2 a+cos^2 a)/cosa.sina
=sin^2 a/cosa.sina + cos^2 a/cosa.sina
=tana+cota

 

[Drongoski]

How does
(sin^2 a+cos^2 a)/cosa.sina = tan a + cot a
unless you put RHS = 1/ cosa.sina
and LHS = 1/cosa.sina

Or does the question allow you to infer?

Here, Timothy.Siu, has avoided temptation to quickly convert sin^2 a + cos^2 a to 1; so instead sin^2/(cos . sin) = sin/cos which is tan and cos^2/(sin . cos) = cos/sin which is cot.

Got it ??

 

[djraven87]

In 2 Unit HSC mathematics when proving trig identities. Do we ONLY prove one side to make it the same as the other. Or do we prove booth sides to a certain form?

Are there some questions in 2 UNIT math that require proving booth sides?

and also just as example how would you do this question? Is it possible to only prove LHS?

sin^2a . tana + cos^2a . cota + 2sina . cosa = tana + cota

sin^2a = (sina)^2

sorry for bad form.

OMG... I do mathematics and i have halfies in a week and i don't understand any of that..

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[Lukybear]

Yea i finally got it. Thxs for enlightening me all of u.

 

[studentcheese]

You pick one side to work with, and try to get to the other side. If you get stuck, then work through both sides.