\operatorname { cos } 105 ^ { \circ } + \operatorname { sin } 105 ^ {

1.	\operatorname { cos } 105 ^ { \circ } + \operatorname { sin } 105 ^ { \circ }
Answer» LHS = sin105° + cos105° = sin(60 + 45 ) + cos ( 60 + 45 ) = ( sin 60 cos 45 + cos 60 sin 45 ) + ( cos 60 cos 45 - sin60 din 45) = { ( √3/2 × 1/√2 ) + ( 1/2 × 1 √2)} + { ( 1/2 × 1√2 ) - ( √3/2 × 1/√2) = ( √3 /2√2 + 1 /2√2 + 1 2√2 + √3 /2√2 ) = 1/√2 = RHS

\operatorname { cos } 105 ^ { \circ } + \operatorname { sin } 105 ^ { \circ }

Answer»

LHS = sin105° + cos105°

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

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

+ ( cos 60 cos 45 - sin60 din 45)

= { ( √3/2 × 1/√2 ) + ( 1/2 × 1 √2)} + { ( 1/2 × 1√2 ) - ( √3/2 × 1/√2)

= ( √3 /2√2 + 1 /2√2 + 1 2√2 + √3 /2√2 ) = 1/√2 = RHS