If #H(y)= cos y - sin y# Show that #H((pi/2) + x) = H(pi-x) = -H (-x)#???

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Answer 1 · 2018-06-18T13:27:10

Given

#H(y)= cos y - sin y#

Putting #y=pi/2+x#

#H(pi/2+x)= cos (pi/2+x) - sin (pi/2+x)#

#=>H(pi/2+x)= -sinx - cosx#

Putting #y=pi-x#

#H(pi-x)= cos (pi-x) - sin (pi-x)#

#=>H(pi-x)= -cos x -sin x#

Putting #y=-x#

#H(-x)= cos (-x) - sin (-x)#

#=>H(-x)= cos x +sin x#

#=>-H(-x)= -cos x - sin x#

So

#H(pi/2+x)=H(pi- x)=-H(-x)#