1.

\operatorname { cos } ( 50 ^ { \circ } + \theta ) \operatorname { cos } ( 20 ^ { \circ } + \theta ) + \operatorname { sin } ( 50 ^ { \circ } + \theta ) \operatorname { sin } ( 20 ^ { \circ } + \theta ) = \frac { \sqrt { 3 } } { 2 }

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