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(a) Prove that sin65^(@)+cos65^(@)=sqrt(...

(a) Prove that `sin65^(@)+cos65^(@)=sqrt(2)cos 20^(@)`
(b) Prove that `sin47^(@)+cos77^(@)=cos17^(@)`

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### Step-by-Step Solution #### Part (a): Prove that \( \sin 65^\circ + \cos 65^\circ = \sqrt{2} \cos 20^\circ \) 1. **Start with the Left-Hand Side (LHS)**: \[ \text{LHS} = \sin 65^\circ + \cos 65^\circ \] ...
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