Question

sin 40° + sin 75° = cos 15 ° + cos 50°

Answer 1

sin 40* + sin (90*-15*) = cos 15* + cos (90*-40*)
sin 40* + cos 15* = cos 15* + sin 40*
L.H.S = R.H.S Proved

Answer 2

It is proven that sin 40° + sin 75° = cos 50° + cos 15°  

Given:

sin 40° + sin 75° = cos 15 ° + cos 50°

To find:

Prove that sin 40° + sin 75° = cos 15 ° + cos 50°

Solution:

Given statement sin 40° + sin 75° = cos 15 ° + cos 50°

Take LHS

sin 40° + sin 75°

As we know

sin (90°- θ) = cos θ  and cos (90°- θ) = sin θ

From above formulas

sin 40° = sin(90-50) = cos 50°

=> sin 40° = cos 50°

sin 75° = sin(90-15) = cos 15°

=> sin 75° = cos 15°  

From above calculations

sin 40° + sin 75° = cos 50° + cos 15°  = RHS

Therefore,

It is proven that sin 40° + sin 75° = cos 50° + cos 15°  

#SPJ2