Question

sin105°+cos105°=cos45°​

Answer 1

Hi ,

LHS = sin 105 + cos105

= Sin( 60 + 45 ) + cos ( 60 + 45 )

= ( sin60cos45+sin45cos60 ) +

( cos60cos45 - sin60sin45 )

= ( √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 )

= 2/2√2

= 1/√2

= Cos45°

= RHS

I hope this helps you.