If sin(x+20)= 2sinx cos40 where x belongs to (0,90) then
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To solve for x : Sin (x + 20°) = 2 sin x cos 40°
We can see that the above equation is valid for x = 30°
as LHS = sin 50°
RHS = 2 sin30° Cos 40° = cos 40° = sin (90° - 40°) = sin 50°
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sinx cos 20 + cosx sin 20 = 2 sin x cos 40
sin x (2 cos 40 - cos 20) = cos x sin 20
Tan x = sin 20 /(2 cos40 - cos20) = 0.5773
=> x = Tan⁻¹ 0.5773 = 30°
We can see that the above equation is valid for x = 30°
as LHS = sin 50°
RHS = 2 sin30° Cos 40° = cos 40° = sin (90° - 40°) = sin 50°
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sinx cos 20 + cosx sin 20 = 2 sin x cos 40
sin x (2 cos 40 - cos 20) = cos x sin 20
Tan x = sin 20 /(2 cos40 - cos20) = 0.5773
=> x = Tan⁻¹ 0.5773 = 30°
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