Question

prove that cos(30°-A) + cos(30°+A) = √3 cosA​

Answer 1

Answer:

cos(30°-A) + cos(30°+A) = √3 cosA

L. H. S

cos(30°-A) + cos(30°+A)

As we know that

Cos(a+b) = cosa*cosb - sina*sinb

Cos(a-b) = cosa*cosb+sina*sinb

Here a=30, b=A

Put it

(cos30*cosA+sin30*sinA) +(cos30*cosA - sin30*sinA)

=> cos30cosA+cos30cosA+sin30sinA-sin30sinA

=> cos30cosA+cos30cosA

=> 2cos30cosA

Here cos30=(3^1/2)/2 put it

2(3)^1/2cosA

(3^1/2)cos A proved