1.

\sin 105^{\circ}+\cos 105^{\circ}=\cos 45^{\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=cos45°


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