If Sinx - Cosx = 1/4 what is the value of Sinx + Cosx ?
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sinx-cosx=1/4
Squaring both sides,
(sinx-cosx)²=1/16
or, sin²x-2sinxcosx+cos²x=1/16
or, 1-2sinxcosx=1/16 [∵, sin²x+cos²x=1]
or, -2sinxcosx=1/16-1
or, -2sinxcosx=(1-16)/16
or, -2sinxcosx=-15/16
or, 2sinxcosx=15/16
Now, (sinx+cosx)²
=sin²x+2sinxcosx+cos²x
=1+2sinxcosx [∵, sin²x+cos²x=1]
=1+15/16
=(16+15)/16
=31/16
∴, sinx+cosx=+-√31/4
Squaring both sides,
(sinx-cosx)²=1/16
or, sin²x-2sinxcosx+cos²x=1/16
or, 1-2sinxcosx=1/16 [∵, sin²x+cos²x=1]
or, -2sinxcosx=1/16-1
or, -2sinxcosx=(1-16)/16
or, -2sinxcosx=-15/16
or, 2sinxcosx=15/16
Now, (sinx+cosx)²
=sin²x+2sinxcosx+cos²x
=1+2sinxcosx [∵, sin²x+cos²x=1]
=1+15/16
=(16+15)/16
=31/16
∴, sinx+cosx=+-√31/4
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