Question

sin A + cos A =1 then prove that sin A- cos A =+-1​

Answer 1

Given that,

sinA + cosA = 1.............(1)

To prove: sinA - cosA= ±1

Squaring (1) on both sides,

(sinA + cosA)²=1

→sin²A + cos²A+2sinAcosA=1

We know that,

sin²∅+cos²∅=1

→2sinAcosA=1-1

→2sinAcosA=0

Now,

sinA - cosA

=√(sinA - cosA)²

=√sin²A + cos²A -2sinAcosA

=√1-0

= ±1

Thus, sinA - cosA = ±1

Hence,proved