Question

Sin5π/18-cos4π/9=√3×sinπ/9

Answer 1

sin(5π/18) - cos(4π/9)  = cos(π/2 - 5π/18) - cos(4π/9), via cofunction identity  = cos(2π/9) - cos(4π/9)  = -2 sin [(1/2)(2π/9 + 4π/9)] sin [(1/2)(2π/9 - 4π/9)], via sum to product identity  = -2 sin(π/3) sin(-π/9)  = -2 * (√3/2) * -sin(π/9), the last factor converted via oddness of sine  = √3 sin(π/9)   Please mark brainliest

Answer 2

LHS=sin5pie/18-cos4pie
=sin 50°-cos80°(converting redain into degrees)
=sin(90-40)°-cos80°
=cos50°-cos80°
=2sin60 sin 20
2sinAsinB=cos(A-B)-cos(A+B)
=2*root3/2 sin 20
=root3sin pie/9
(converting degrees in radian)
LHS=RHS......

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