Question

prove that sin a + b into Sin A minus b equal to sin square A minus sin square B​

Answer 1

Step-by-step explanation:

Sin(a+b) * Sin(a-b)

(Sina*Cosb+Cosa*Sinb)(Sina*Cosb-Cosa*Sinb)

(Sina*Cosb)² - (Cosa*Sinb)²

Sin²a * Cos²b - Cos²a * Sin²b

Sin²a(1-Sin²b) - Cos²a*Sin²b

Sin²a - Sin²a*Sin²b - Cos²a*Sin²b

Sin²a - Sin²b(Sin²a + Cos²a)

Sin²a - Sin²b(1)

Sin²a - Sin²b

Answer 2

\sin^2A\cos^2B-\cos^2A\sin^2B=\sin^2A-\sin^2B proved.

Step-by-step explanation:

Consider the provided information.

\sin^2A\cos^2B-\cos^2A\sin^2B=\sin^2A-\sin^2B

Consider the LHS.

\sin^2A\cos^2B-\cos^2A\sin^2B

\sin^2A(1-\sin^2B)-(1-\sin^2A)\sin^2B               (∴\cos^2x=1-\sin^2x)

\sin^2A-\sin^2A\sin^2B-\sin^2B+\sin^2A\sin^2B

\sin^2A-\sin^2B

Hence, proved.