Question

prove :-
sin(105)+ cos(105)=cos(45)

Answer 1

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please refer to the attachment above....


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Answer 2

Taking LHS:

sin 105° + cos 105°

cos (90° - 105°) + cos 105°

cos 15° + cos 105°

cos C + cos D = 2(cos(C+D)/2)(cos(C-D)/2)

2cos(120°/2)cos(90°/2)

2cos60°cos45°

2(1/2)cos45°

cos45°

= RHS



sin 105° + sin (90° – 105°)

sin 105° - sin 15°

sin C - sin D = 2(cos(C+D)/2)(sin(C-D)/2)

2cos(120°/2)sin(90°/2)

2cos60°sin45°

2(1/2)sin45°

sin 45°

= cos 45°

= RHS