Question

Show that (sinA + COSA)^2+(sin A -cos A)^2 = 2
​

Answer 1

Step-by-step explanation:

(sinA+cosA)² +(sinA-cosA)²

=sin²A+cos²A+2sinAcosA+sin²A+cos²A-2sinAcos

since sin²A+cos²A=1

1+2sinAcosA+1-2sinAcosA

=1+1

=2

Answer 2

To prove:

( sin A + cos A) ² + ( sin A - cos A) ² = 2

Proof:

LHS

( sin A + cos A) ² + (sin A - cos A) ²

........... Using (a+b) ² = a² + 2ab + b²

........... Using (a-b) ² = a² - 2ab + b²

(sin A² + 2 sinA cosA + cos A²) + (sin A² - 2 sinA cosA + cos A²)

.......... + 2 sinA cosA and - 2 sinA cosA gets cancelled because of + and - sign

sin A² + cos A² + sin A² + cos A²

.......... Trigonometry identity.... sin A² + cos A² = 1

1 + 1

= 2

Therefore LHS = RHS = 2

Hence we proved that.....

( sin A + cos A) ² + (sin A - cos A) ² = 2

✔️Pls mark it brainliest.. ✔️