Sin cos cos 2 2 2 2 cos sin 2 2 cos2 sin hence 2 2 2

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Unformatted text preview: ∂ ∂2 ∂ ∂2 ∂ + ∂ 2∂ ∂∂ ∂ 2 ∂ ∂2 2 cos2 + ∂2 ∂∂ ∂ ∂ ∂ sin cos + ∂ cos + 2 ∂ ∂ ∂2 ∂ ∂2 ∂ ∂ +2 sin + sin = ∂∂ ∂ ∂∂ ∂ ∂2 ∂2 ∂ 2 cos + cos sin + 2 2 sin2 + sin ∂∂ ∂ ∂ cos + and ∂∂ ∂∂ ∂ ∂2 = = (− sin ) + cos = 2 ∂ ∂∂ ∂ ∂ ∂ ∂∂ ∂ ∂ ∂∂ (− cos ) + (− sin ) = (− sin ) + cos + ∂∂ ∂ ∂∂ ∂ ∂2 ∂ ∂2 ∂ ∂ + (− sin ) + (− cos )+ 2∂ ∂ ∂∂ ∂ ∂ ∂2 ∂ ∂ ∂2 ∂ +2 cos + (− sin ) = ∂∂ ∂ ∂∂ ∂ ∂2 2 ∂2 ∂ 2 sin2 − sin cos − cos − 2 ∂ ∂∂ ∂ ∂2 ∂2 ∂ 2 cos sin + 2 2 cos2 − sin ∂∂ ∂ ∂ Hence −2 ∂2 ∂ 2 ∂2 ∂2 +2= ∂2 ∂ ∂2 ∂− ∂2 ∂2 ∂ cos2 + sin cos + cos + cos sin + 2 sin2 + ∂∂ ∂ ∂∂ ∂ ∂ 2 2 ∂ ∂ ∂− sin2 − sin cos − cos − 2 ∂ ∂∂ ∂ ∂2 ∂2 ∂− cos sin + 2 cos2 − sin = ∂∂ ∂ ∂ ∂2 ∂2 ∂2 (cosθ + sinθ ) + 2 (sin2 θ + cos2 θ ) = ∂2 ∂ ∂ 4 − sin + 2 + ∂2 ∂2 :) Please feel free to use less cumbersome notation though... E Substit...
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