Question

25.
If cosx+sin x = 12 cos x, show that cosx-sin x = V2 sinx.​

Answer 1

cosx+sinx=2cosx

Squaring both sides, we get

cos2x+sin2x+2cosxsinx=2cos2x

2cosxsinx=cos2x−sin2x

2sinxcosx=(cosx+sinx)(cosx−sinx)

(cosx−sinx)2sinxcosx=(cosx+sinx)

(cosx−sinx)2sinxcosx=2cosx

⇒cosx−sinx22sinx=2×2

⇒cosx−sinx22sinx=2

∴cosx−sinx=2sinx

Answer 2

Step-by-step explanation:

cos x + sinx = V2 cosx

squaring both sides

1+ Sin2x = 2 Cos^2x

1- Sin2x = 2 - 2 Cos^2x

( cosx + SinX)^2= 2 Sin^2 x

Cos X + SinX =V2 SinX