Question

If sina– cosa = 1, prove that sina+ cosa = 1
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Answer 1

Step-by-step explanation:

use identity sin²A+cos²A=1

given sinA-cosA=1

sin²A-cos²A=1

(sinA-cosA)(sinA+cosA)=1

1(sinA+cosA)=1

sinA+cosA =1

Hence proved

Answer 2

Step-by-step explanation:

$sinA - cosA=1$                                       (given)

$sin^{2} A$$-2cosAsinA+$$cos^{2} A$=1                     (by squaring both sides)

$1-2cosAsinA$=$1$          

$2cosAsinA$=$0$

$Substitute$ $in$ $sinA + cosA$

$sin^{2} A$+$2cosAsinA$+$cos^{2} A$

$=1+0=1$

$L.H.S. = R.H.S.$