Question

if sinA/x=cosA/y then prove that sinA-cosA=x-y/√x²+y²​

Answer 1

Answer:

sinA/x = cosA/y

or, sinA/cosA =x/y

By addendo- dividendo we get,

or, (sinA + cosA)/(sinA-cosA)= (x+y)/(x-y)…1

Again, sin²A/cos²A= x²/y²

By addendo- dividendo we get,

(sin²A+cos²A)/(sin²A-cos²A) = (x²+y²)/(x²-y²)

or, 1/(sinA+cosA)(sinA-cosA)=(x²+y²)/(x²-y²)

Putting the value of (sinA+cosA) from equation 1, we get

(x-y)/(sinA-cosA)(sinA-cosA)(x+y)=

(x²+y²)/(x²-y²)

or, (sinA-cosA)²= (x-y)(x²-y²)/(x+y)(x²+y²)

or,(sinA-cosA)²= (x-y)²/(x²+y²)

or, sinA-cosA= (x-y)/√(x²+y²)[Proved