Question

sin105 + cos105=cos45

Answer 1

sin105+cos105= cos45
sin(60+45)+cos(60+45)=1/√2
sin60cos45+cos60sin45+
cos60cos45-sin60sin45= 1/√2
√3/2 *1/√2 + 1/2 * 1/√2 + 1/2 * 1/√2 - √3/2 * 1/√2 = 1/√2
1/2√2 + 1/2√2= 1/√2
2/2√2= 1/√2
1/√2= 1/√2 ans

Answer 2

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.

:)