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Question

Show that sin 105 + cos105 = 12

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Solution

We have LHS = sin 105 + cos105

= sin (60+45) + cos (60+45)

= (sin 60cos 45+cos 60sin 45) + (cos 60 cos 45 - sin 60sin 45)

={(32×12)+(12×12)}+{(12×12)(32×12)}

=(322+122+122322)=12 = RHS.


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