Sin 1o5 °- Сos 105° = cos4 5°
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Step-by-step explanation:
taking L.H.S
sin 105 - cos 105
sin ( 180 - 75 ) - cos ( 180 - 75 )
sin 75 - [ - cos 75 ] { sin x is positive in second quadrant and cos x is negative in second quadrant }
sin 75 + cos 75
sin 75 + sin ( 90 - 15 )
sin 75 + sin 15
Applying formula [ sin C + sin D = 2 sin ( C + D )/2 sin ( C - D ) /2. ]
on comparing we have ,
2 sin ( 75 + 15 ) /2 sin ( 75 - 15 ) /2
2sin 45 sin 30
putting values ,
2 * ( 1 /√2 ) * 1/2
1/√2
taking R.H.S
cos 45
1/√2
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