Solve the inequation for x :
 
Sin^2 X > Cos^2 X

Asked by sudhanshubhushanroy | 19th Nov, 2017, 10:08: AM

Expert Answer:

begin mathsize 16px style sin squared straight x greater than cos squared straight x
open parentheses sinx minus cosx close parentheses open parentheses sinx space plus cosx close parentheses greater than 0
so space Case space 1 colon open parentheses sinx minus cosx close parentheses greater than 0 space and space open parentheses sinx space plus cosx close parentheses greater than 0
Case space 2 space colon space open parentheses sinx minus cosx close parentheses less than 0 space and space open parentheses sinx space plus cosx close parentheses less than 0
in space case space 1
open parentheses sinx minus cosx close parentheses greater than 0
sinx greater than cosx
sinx space greater than space sin open parentheses straight pi over 2 minus straight x close parentheses
straight x greater than open parentheses straight pi over 2 minus straight x close parentheses
straight x greater than straight pi over 4..... left parenthesis 1 right parenthesis
open parentheses sinx plus cosx close parentheses greater than 0
sinx greater than negative cosx
sinx space greater than space minus sin open parentheses straight pi over 2 minus straight x close parentheses
straight x greater than open parentheses negative straight pi over 2 plus straight x close parentheses
0 greater than negative straight pi over 2.... true space for space all space straight x element of straight R.... left parenthesis 2 right parenthesis
left parenthesis 1 right parenthesis space intersection space left parenthesis 2 right parenthesis.... space gives space straight x greater than straight pi over 4
similarly space solve space for space case space 2

end style

Answered by Arun | 1st Dec, 2017, 05:45: PM