Question

prove that (casA+sinA)²+(cosA-sinA)²=2​

Answer 1

L.H.S

$\implies(cosA+ sinA)^{2}+(cos+sinA)^{2}$

$\implies(cos^{2} + sin^{2})+(cos^{2} + sin^{2})$

$\implies(1) + (1)$

$\implies \: 2 \: = R.H.S$

plz mark me as brain list.

Answer 2

Step-by-step explanation:

We know that,

(x + y)² = x² + 2xy + y²

(x - y)² = x² - 2xy + y²

Now,

LHS = (CosA + SinA)² + (CosA - SinA)²

RHS = 2

Now,

LHS = (CosA + SinA)² + (CosA - SinA)²

Using the algebraic identities,

(Cos²A + 2CosASinA + Sin²A) + (Cos²A - 2CosASinA + Sin²A)

Opening the Brackets we get,

Cos²A + 2CosASinA + Sin²A + Cos²A - 2CosASinA + Sin²A

Sin²A + Cos²A + Sin²A + Cos²A + 2CosASinA - 2CosASinA

We know that,

Sin²A + Cos²A = 1

Thus,

(Sin²A + Cos²A) + (Sin²A + Cos²A)

= 1 + 1

= 2 = RHS

∴ LHS = RHS

Hence proved.

Hope it helped and believing you understood it........All the best