sin^2(5) + sin^2(10) +............+sin^2(90)/(1+cos^2(5) + cos^2(10)......cos^2(90)) = ?

Question

sin^2(5) + sin^2(10) +............+sin^2(90)/(1+cos^2(5) +  cos^2(10)......cos^2(90)) = ?

unklerhaukus · Answer

$$\frac{\sin^2(5) + \sin^2(10) +............+\sin^2(90)}{1+\cos^2(5) +  \cos^2(10)......\cos^2(90) }= ?$$

anonymous · Answer

yes

anonymous · Answer

@UnkleRhaukus  help

unklerhaukus · Answer

i can't see a good first step  yet.
maybe use a trig formula

unklerhaukus · Answer

are they ment to be more terms in the numerator than the denominator?

anonymous · Answer

there  is 1 in deno

unklerhaukus · Answer

i mean more in the denominator than the numerator, 
actually i guess the is an invisible $\sin(0)$ in the numerator so they have the same number of terms

unklerhaukus · Answer

the 1 is a really a  $\cos(0)$

anonymous · Answer

no

anonymous · Answer

sorry but there is   sin^2(85) in numerator    and       cos^2(85) in denominator

anonymous · Answer

@UnkleRhaukus

unklerhaukus · Answer

$$=\frac{\sum\limits_{n=0}^{18}\sin(5n)}{\sum\limits_{n=0}^{18}\cos(5n)}$$

ujjwal · Answer

Add a sin^2 (0) to numerator. And in denominator, 1=cos^2 (0).

Now, Sin^2 theta = cos^2 (90-theta)

Proceed yourself further.

experimentx · Answer

sin(5) = cos(85)

they are symmetric about 45 ... use these to get 1's

anonymous · Answer

so  wat will we get

experimentx · Answer

(1 + 1 + 1 + ... +1 + 1/sqrt(2))/(1 + 1 + 1 + ... +1 + 1/sqrt(2)) = 1
my guess ... haven't worked out ... must be 9 1's

precal · Answer

you are in good hands, can't help you at the moment

anonymous · Answer

the asnwer should be 1

anonymous · Answer

@experimentX

experimentx · Answer

yeah i guessed that ... i also gave you hint how to solve ... it's too long to type..

ujjwal · Answer

The answer is one. you have already got the process.. 
Its amazing to see how similar you are to shameer and openstudy1.

ujjwal · Answer

Try it yourself.

anonymous · Answer

s i will try

anonymous · Answer

i got answer as 1/2..........@experimentX

anonymous · Answer

@experimentX

experimentx · Answer

you shouldn't get that 
sin^2(5) + sin^2(10) +............+sin^2(90 = 

sin^2(0) + sin^2(90) + sin^2(5) + sin^2(85) +............+sin^2(40)+sin^2(50) + sin^2(45)

first arrange like this and get 9 + 1/sqrt(2)
do same for denominator

anonymous · Answer

@experimentX  9 + 1/2 for the numerator and the denominator. You forgot to 
square 1/sqrt(2).

experimentx · Answer

Oh ... thanks for correcting prof!!

experimentx · Answer

lol ... silly me!!