Trigonometry Help (1 Viewer)

[od9895]

Hi
Could someone please explain to me how to do these questions

Simplify
1. cosec^2a - 1/tan^2a
2. 1/tan^2a + 1-cos^2a/sin^2a
3.cosa+sina/cosa-sina + cosa - sina/cosa+sina

21. If tanA =4 and tanB=3/5 and A and B are acute angles, prove without using tables that A-B=45

22. If tana =4/3 and cosB= 1/13 where 0<B<a<90, evaluate without using tables
a) sin2a
b) tan2a
c)cos(a-B)

Please show all working so I could write these questions and solutions in my revision notes.

Thanks

 

[Drongoski]

3) ??





Someone else - please do the rest.

 

[SpiralFlex]

3) ??

I would assume Q3 is set out such that a student will see and make use of the famous identity of

 

[Demento1]

Um, bearing in mind i'm only a year 10 student so I seriously don't know what LATEX is other then the fact it is a program i'll try to write Q3 working out for you.

cosa+sina / cosa-sina + cosa - sinA / cosa+sina

= (cosa+sina)^2+(cosa-sina)^2 / cos^2a-sin^2a -----Cross multiply the fractions

= 2cos^2a+2sin^2a / cos^2a-sin^2a -----Expand and simplify

= 2(cos^2a+ sin^2a) / cos^2a-sin^2a -----Factorise whenever you can

= 2 / cos^2a - sin^2a -----Notice that cos^2a + sin^2a = 1 (Spiral mentioned it)

DONE

 

[Pfortune35]

Um, bearing in mind i'm only a year 10 student so I seriously don't know what LATEX is other then the fact it is a program i'll try to write Q3 working out for you.

cosa+sina / cosa-sina + cosa - sinA / cosa+sina

= (cosa+sina)^2+(cosa-sina)^2 / cos^2a-sin^2a -----Cross multiply the fractions

= 2cos^2a+2sin^2a / cos^2a-sin^2a -----Expand and simplify

= 2(cos^2a+ sin^2a) / cos^2a-sin^2a -----Factorise whenever you can

= 2 / cos^2a - sin^2a -----Notice that cos^2a + sin^2a = 1 (Spiral mentioned it)

DONE

keeping in mind cos 2a = cos^2 a - sin^2a we could say

the final answer is also 2/ cos 2a

 

[nightweaver066]

keeping in mind cos 2a = cos^2 a - sin^2a we could say

the final answer is also 2/ cos 2a

Or 2sec2a lol

 

[Demento1]

keeping in mind cos 2a = cos^2 a - sin^2a we could say

the final answer is also 2/ cos 2a

Sorry, forgot to add in from:

= 2 / cos^2a - sin^2a

= 2 (sec^2a - cosec^2a)

@Pfortune35: Sorry, my knowledge on identities is limited to pythagoras so I haven't heard of the formula you mentioned above unfortunately. Though of course, i'll look that up!

 

[Demento1]

Ahh yep, just learnt another new formula. So of course, the answer is what night weaver said: 2sec2a

 

[such_such]

Here is it kinda nicely simplified Sorry my scanner is old, and I rushed this so it could contain mistakes.

 

[nightweaver066]

Here is it kinda nicely simplified Sorry my scanner is old, and I rushed this so it could contain mistakes.


View attachment 24215

Your writing... Looks so much like someone i know.. But they're a guy.

 

[Demento1]

Hmm, i believe most mathematicians have very ugly writing...

 

[Carrotsticks]

Here is it kinda nicely simplified Sorry my scanner is old, and I rushed this so it could contain mistakes.

I'm having trouble processing this.

Also, your handwriting is absolutely fabulous. I'm repping you just for that.

Your writing... Looks so much like someone i know.. But they're a guy.

Who said such_such isn't a guy? Guys can also have pink sigs.

Hmm, i believe most mathematicians have very ugly writing...

 

[nightweaver066]

I'm having trouble processing this.

Also, your handwriting is absolutely fabulous. I'm repping you just for that.



Who said such_such isn't a guy? Guys can also have pink sigs.

Manly.

And i just went to such_such's profile and it is indeed a girl.

 

[Carrotsticks]

I was watching this very stupid video earlier today. Something about analysing a person's personality through their handwriting only.

According to that video, I have homicidal tendencies, so you guys better watch out

 

[Demento1]

I was watching this very stupid video earlier today. Something about analysing a person's personality through their handwriting only.

According to that video, I have homicidal tendencies, so you guys better watch out

I would imagine that video to be true to some extent. So unfortunately, mathematicians are born to be criminals it would seem

Also, do you have a link of the video, carrotsticks? I'm actually interested to watch that stuff considering my boredom in the holidays.

 

[IamBread]

Hmm, i believe most mathematicians have very ugly writing...

My maths teacher last year had very neat handwriting. Mine is ok, looks like Carrotsticks tbh lol.

I was watching this very stupid video earlier today. Something about analysing a person's personality through their handwriting only.

According to that video, I have homicidal tendencies, so you guys better watch out

Haha where did you find this video? I'd like to see what my personality is