Question

(iii) cos (60° + a) sin (60° - a) = 1/4( √ 3 _2 sin a)
​

Answer 1

Answer:

correction=> RHS= 1/4(√3-2sin2a)

Step-by-step explanation:

LHS

cos(60+a)sin(60-a)

[(1/2)cos a - (√3/2)sin a] [ (√3/2)cos a - (1/2)sin a]

(1/4) [ cos a- √3 sin a] [ √3cos a- sin a]

(1/4) [ √3 cos²a- sin a cos a-3sin a cos a+√3 sin²a]

(1/4) [ √3(sin²a+cos²a) - 4 sinacosa]

(1/4)[ √3×1 - 2sin 2a]

(1/4) [ √3 -2 sin2a]

= RHS

formula used

(1) sin(A-B) sinAcosB-cosAsinB

(2) cos(A+B) = cosAcosB- sinAsinB

(3) sin²A+cos²A = 1

(4) 2sinAcosA = Sin2A

hope this helps you