Question

✓sin x + cos x =0 then sin x=0​

Answer 1

Answer:

√sinx+cosx=0

√sinx= -cosx

squaring,

sinx=cos^2x=1-sin^2x

sinx+sin^2x=1

completing square on LHS,

sin^2x+sinx+1/4=1+1/4

(sinx+1/2)^2=(√5/2)^2

sinx+1/2=+ or- √5/2

sinx=-1/2 + or-√5/2

but because of √sinx,sinx less than 0 is not

admissible

therefore,

sinx=-1/2+√5/2=√5-1/2