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[tex] \sin(25) \cos(65) + \cos(25) \sin(65) [/tex]
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[tex]\huge\boxed{\fcolorbox{purple}{ink}{Question}}[/tex]
[tex] \sin(25) \cos(65) + \cos(25) \sin(65) [/tex]
( Quality answers)
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as sin theta=cos(90-theta)
so sin 25=cos(90-25)=cos 65
likewise
as cos theta=sin(90-theta)
so cos 25=sin(90-25)=sin 65
therefore
sin(25)cos(65) + cos(25)sin(65)
cos(65)cos(65) + sin(65)sin(65)
cos²(65) + sin²(65) = 1
from identity sin²theta+cos²theta=1