ISI 2005

this is the complete question.....all solutions..no options given...have to show the steps.....

x belongs to {2n∩,2n∩+∩/2}

abhi bhai cosx mein cubic ban jaaegi
meand it should have 3 roots
x=0
x=pi/2
x=?????
bas aakhri waala reh gaya

cubic cosx mein aaegi

just write sin⁵x as sin²x X sin³x
then use sin²x=1-cos²x

write 1 as sin²x + cos²x

sinx be s
cosx be c

s² + c² =1

now as s,c≤1

with higher powers obvious either s or c =1

Awesome cele!

great!