Question

-1≤sinx≤1 Prove that​

Answer 1

Answer:

Let sinx=a & cosx=b

So,

a+b=1

We know that,

sinx^2+cosx^2=1

a^2+b^2=1

(a+b)^2=a^2+b^2+2ab

(1)^2=1+2ab

1=1+2ab

2ab=0

(a-b)^2=a^2+b^2-2ab

(a-b)^2=1-0

(a-b)^2=1

a-b=+-1

sinx-cosx=+-1