MEDALS!

Question 8 without using angle sum identities.

This is a screening test for a summer course for linear algebra in Hong Kong University. I was lucky as I thought that they would ask questions on trigonometry so I memorised the angle sum identities in the last minute. I think I got this right and I am curious on how to do question 8 without the identities.

Question

MEDALS!

Question 8 without using angle sum identities.

This is a screening test for a summer course for linear algebra in Hong Kong University.  I was lucky as I thought that they would ask questions on trigonometry so I memorised the angle sum identities in the last minute.  I think I got this right and I am curious on how to do question 8 without the identities.

thomas5267 · Answer

Question 8:

anonymous · Answer

@BSwan

anonymous · Answer

why dnt you type a question at once xD
:'(

anonymous · Answer

question 1
$\sum_{n=1}^{n} (n+1) 2^{n-1}=n2^n$
by induction :-

$\color{red}{\text {STEP 1:-}}$
for n=1
2=2 its correct

$\color{red}{\text {STEP 2 :-}}$
assume its true for k
$\sum_{k=1}^{k} (k+1) 2^{k-1}=k2^k$

$\color{red}{\text {STEP 3 :-}}$
show its true for k+1 
:P can u do it ?

anonymous · Answer

the question is to evaluate sin(p+q)
why would you wanna go long way though

anonymous · Answer

@BSwan  he wants question 8 :P

anonymous · Answer

sorry for the wasted efforts xD

anonymous · Answer

O.O

anonymous · Answer

i hate u @aajugdar

anonymous · Answer

whaaa
he mentioned he wants question 8 xD you didnt read

thomas5267 · Answer

I finally got question 6 right after three trials.  *sigh*  Wasted quite a lot of time... :(

ganeshie8 · Answer

haha u gave right answer to a wrong question @BSwan  :P

thomas5267 · Answer

I mean in the test.

anonymous · Answer

:D

anonymous · Answer

its my bad i dint read lol

anonymous · Answer

so stil wanna  8 ?

anonymous · Answer

@BSwan  he wants to solve it without using trigonometry

anonymous · Answer

andd i hv no clue why o_o

thomas5267 · Answer

Yep.  I want to know how people can solve this without the identity.

thomas5267 · Answer

I was lucky as I memorised the identity in the last minute (literally five minutes before the test).  I just want to know how others can solve it.

anonymous · Answer

wew !
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ganeshie8 · Answer

so the bottom triangle is a 3,4,5 triangle

thomas5267 · Answer

I think the tricky bit is how to draw a triangle with p+q as one of the angles.

anonymous · Answer

is m parallel to f ?
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thomas5267 · Answer

But not everyone in the test knows the identity so there must be a way solving it without using the identity.  (ah... I know it is faulty logic but I just want the answer lolololol)

ganeshie8 · Answer

yes @BSwan  there is no harm in constructing a parallel line to f, its perfectly valid

anonymous · Answer

:D
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