Question

sin40-cos70=√3cos80
please help me prove this

Answer 1

Write sin40° as cos50° and apply cosC – cosD =[2Sin{(C+D)/2}sin{(D–C)/2}]. Which will give u √3sin10° and sin10°=cos80° . hence proved..
Mark as brainliest

Answer 2

hello users.....

we have to prove that:
sin40°-cos70°=√3cos80°

solution:-
formula used;
sin (90° - x ) = cos x
&
cos C - cos D = 2 sin { ( C+ D) /2 } sin { D -C ) /2}

Here,
Taking LHS ;
sin40°-cos70°

= sin (90° - 50° ) - cos 70°
= cos 50° - cos 70°

=> 2 sin { (50°+70°)/2 } sin {(70°-50°)/2}

=> 2 sin 60° sin 10°

=> 2×√3/2 × sin 10° .(sin 60°=√3/2)

=> √3 × sin (90° -80°)

=> √3 cos 80° = RHS

Hence;
Proved ......

⭐✡ hope it helps ✡⭐