Question

if Sin theta +cos theta =X,sin theta-costheta =y.prove that x2+y2=2




plzz.. solve it correct​

Answer 1

HEY MATE!!!

sin theta/x = cos theta/y

sin theta/cos theta = x/y

tan theta = x/y 

sin theta = x/root(x2+y2) and cos theta 

y/root(x^2+y^2)

sin theta – cos theta = (x-y)/root(x^2+y^2)

HOPE IT HELPS YOU!!!

Answer 2

Hey! Here's your answer:

(Denoting 'theta' with 'A' here)

Given: sinA+cosA=x

squaring both sides:

(SinA+cosA) ^2=x^2

=sin^2A+cos^2A+ 2sinAcosA =x^2

>>1+ 2sinAcosA=x^2----------- Eq-1

(By trigonometric identity sin^2A+cos^2A=1)

also given: sinA-cosA=y

Similarly on squaring both sides:

=sin^2A+cos^2A- 2sinAcosA =y^2

>>1-2sinAcosA=y^2----------- Eq-2 (sin^2A+cos^2A=1)

Hence, on adding Eq-1 and Eq-2:

1+ 2sinAcosA=x^2

1-2sinAcosA=y^2

________________

1+1            = x^2+y^2

________________

therefore, x^2+y^2=2

HENCE PROVED.

HOPE I WAS ABLE TO HELP!!