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Prove that (i) " sin " (50^(@) + the...

Prove that
`(i) " sin " (50^(@) + theta ) " cos " (20^(@) + theta) - " cos " (50^(@) + theta) " sin " (20^(@) + theta) =(1)/(2)`
`(ii) " cos " (70^(@) + theta ) " cos " (10^(@) + theta ) + " sin " (70^(@) + theta) " sin " (10^(@) + theta)=(1)/(2)`

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To prove the given trigonometric identities, we will use the sine and cosine subtraction formulas. ### (i) Prove that: \[ \sin(50^\circ + \theta) \cos(20^\circ + \theta) - \cos(50^\circ + \theta) \sin(20^\circ + \theta) = \frac{1}{2} \] **Step 1: Apply the sine subtraction formula.** ...
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