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Question : 23 of 120
Marks:
+1,
-0
Solution:
cos2x+cos2y−2‌cos‌x‌cos‌y cos(x+y)
=cos2x+cos2y−2‌cos‌x‌cos‌y [cos‌x‌cos‌y−sin‌x‌sin‌y]
=cos2x+cos2y−2cos2xcos2y +2‌sin‌x‌sin‌y‌cos‌x‌cos‌y
=cos2y−cos2xcos2y+cos2x−cos2ycos2x +2‌sin‌x‌sin‌y‌cos‌x‌cos‌y
=(1−cos2x)cos2y+(1−cos2y)cos2x +2‌sin‌x‌sin‌y‌cos‌x‌cos‌y
=sin2xcos2y+cos2xsin2y +2‌sin‌x‌sin‌y‌cos‌x‌cos‌y
=[sin‌x‌cos‌y+cos‌x‌sin‌y]2
=[sin(x+y)]2
=sin2(x+y)
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