Question

Sin 1o5 °- Сos 105° = cos4 5°​

Answer 1

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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