2015
Mathematics
67ca00ce0c643c71d77dee1f
If x + y = 90 simplify (sinx+siny)2 −2sinxsiny
A.
1
B.
0
C.
2
D.
-1
Correct Answer: 1
Explanation
Given: x + y=90°...(1) (sinx + siny)2 −2sinxsiny = sin2 x + sin2 y + 2sinxsiny − 2sinxsiny = sin2 x + sin2 y...(2) Recall: sinx = cos(90−x)...(a) From (1), y = 90−x...(b) Putting (a) and (b) in (2), we have sin2 x + sin2 y ≡ cos2 (90−x) + sin2 (90−x) = 1
Given: x + y=90°...(1) (sinx + siny)2 −2sinxsiny = sin2 x + sin2 y + 2sinxsiny − 2sinxsiny = sin2 x + sin2 y...(2) Recall: sinx = cos(90−x)...(a) From (1), y = 90−x...(b) Putting (a) and (b) in (2), we have sin2 x + sin2 y ≡ cos2 (90−x) + sin2 (90−x) = 1THIS WEEK's
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