Question

prove that. sin 105° + cos 105°= cos 45°​

Answer 1

Answer:

Step-by-step explanation

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

I could also have converted to sine:

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