sin X + cos X=root2 sin(pi/4+theta)

 

sin X + cos root 2 <pi/2                         as root 2=1.414 and pi/2=1.57

sinX  + cos X<pi/2

cos X<pi/2-sin X.........................(1)

 

takin sin on both sides of equation 1 we get the required result

 

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