Find the value of-

 Find the value of

 Hint: Multiply and divide by sin1

http://www.goiit.com/posts/list/algebra-remainder-1126596.htm

hey i did it by the way of congruences.....

i am working on this one.

 Ya I saw it on AoPS. By the way I'm still a beginner in congruences. Can you suggest a nice website to learn it?

1/[sin45*sin46] + 1/[sin47*sin48] + …………. 1/[sin133*sin134]

Or, (1/sin1) {sin1/[sin45*sin46] + sin1/[sin47*sin48] + …………. +Sin1/[sin133*sin134]}

Or, (1/sin1) {sin(46-45)/[sin45*sin46] + sin(48-47)/[sin47*sin48] + …………. +Sin(134-133)/[sin133*sin134]}

Or,  (1/sin1) {(sin46cos45-cos46sin45)/[sin45*sin46] + (sin48cos47-cos48sin47)/[sin47*sin48] + …………. +(sin134cos133-cos134sin133)/[sin133*sin134]}

Or, (1/sin1){ cot45 – cot46 + cot47 – cot48 + ………..+ cot133 – cot134}

Or, (1/sin1){ cot45 – cot46 + cot47 – cot48 + ……+cot89 – cot90 + cot91 – cot92…..+ cot133 – cot134}

Also cot(180-x) = - cotx

Or, (1/sin1){ cot45 – cot46 + cot47 – cot48 + ……+cot89 – cot90 –cot89 +cot88…..- cot47 + cot46}

Or, (1/sin1) ( cot45 – cot90)

Or, (1/sin1) answer……….

https://www.codecogs.com

this will help you with the latex thing. :-)

it is awesome...

and for that congruences thing i would say try to solve the thousands of problems on Aops...

which book you use? i mean for mathematics apart from iitjee??

 check your dashboard. i dont think it would be appropriate to have a conversation over here.

hemang has already solved the question!