Question

Prove the following sin 40 degree minus Cos 70 degree equal to 3 cos 80 degree​

Answer 1

Hey Mate!! Here is your answer.....

Step-by-step explanation:

LHS =sin40-cos70

=sin40-cos(90-20)

=sin40-sin20

now use formula

sinA-sinB=2cos(A+B)/2.sin(A-B)/2

hence.

sin40-sin20=2cos30.sin10

=2 x √3/2 x cos80

=√3cos80° =RHS

LHS = RHS: Hence Proved!

Hope it helps as it took lots of time. Please mark as brainliest!!!

My answer was first and I think it is correct. Please mark as brainliest

Answer 2

Answer:

Step-by-step explanation:

sin A = sin(180 - A)

cos A = sin(90 - A)

sin A - sin B = 2 cos((A + B)/2) sin((A - B)/2))

sin A = -sin(-A)

cos A = -cos(180 - A)

cos 30 = √3 /2

sin 40 - cos 70

= sin 140 - sin 20

= sin 140 - sin 160

= 2 cos( (140 + 160)/2) sin( (140 - 160)/2 )

= 2 cos 150 sin(-10)

= -2 cos 150 sin 10

= -2(-cos 30) sin 10

= 2 cos 30 sin 10

= 2 cos 30 cos 80

= 2(√3 /2) cos 80

= √3 cos 80