Simplify the expression:

\((1+\sin y)(1+\sin(-y))=\cos^2 y\)

( 1 + s in y ) ( 1 + s in ( − y )) = co s 2 y L = ( 1 + s in y ) ( 1 − s in y ) = 1 2 − s i n 2 y = 1 − s i n 2 y = co s 2 y R = co s 2 y L = R
s in ( − x ) = − s in x s i n 2 x + co s 2 x = 1 → 1 − s i n 2 x = co s 2 x ( a + b ) ( a − b ) = a 2 − b 2

Answered by Anonymous | 2024-06-10

sin (-x) = - sin x sin^2+cos^2=1
(1+siny)(1-siny)=cos^2y 1-sin^2=cos^2y cos^y=cos^2

Answered by HannahN | 2024-06-10

The expression ( 1 + sin y ) ( 1 + sin ( − y )) = cos 2 y can be simplified by recognizing that sin ( − y ) = − sin y . This leads to ( 1 + sin y ) ( 1 − sin y ) = cos 2 y , confirming the identity using the Pythagorean identity. Thus, the equation holds true.
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Answered by Anonymous | 2024-10-15