Question

Prove that sin 105 degree + cos 105 =1 by root two

Answer 1

Hi ,

1 )sin 105

= sin( 60 + 45 )

= sin60cos45 + cos60sin45

= ( √3/2 )( 1/√2 ) + ( 1/2 )( 1/√2 )

= √3/2√2 + 1/2√2

= ( √3 + 1 )/2√2 ---( 1 )

cos 105

= cos ( 60 + 45 )

= cos60 cos45 - sin60 sin45

= ( 1/2 )( 1/√2 ) - ( √3/2 )( 1/√2 )

= ( 1/2√2 ) - ( √3/2√2 )

= ( 1 - √3 )/2√2 -----( 2 )


Now ,

sin 105 + cos 105

= ( √3 + 1 )/2√2 + ( 1 - √3 )/2√2

= [ √3 + 1 + 1 - √3 ]/2√2

= 2/2√2

= 1/√2

I hope this helps you.

: )

= √3/√2

Answer 2

Hi,

Please see the attached file!



Thanks