The missing term are sin y and cos y , Option C and D is the correct answer.
Trigonometric Identities are the equations that are true for every variables .
To prove , sin( x+y) = cos y sin x +cos x siny
cos ((π/2) - (x+y)) = sin (x+y)
cos ( x - y) = cos x cos y - sin x sin y
cos (( (π/2) - x) - y)
= cos ((π/2) -x) cos y + sin y sin ((π/2) - x)
= sin x cos y + sin y cos x
Therefore , the missing term are sin y and cos y , Option C and D is the correct answer.
The complete question is
Use the drop-down menus in the derivation of the sine sum identity:
sin( x+y) = ____ sin x +cos x ___
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