Find value of x, if :
tan x = tan 60° - tan 30°1 + tan 60° tan 30°\dfrac{\text{tan 60° - tan 30°}}{\text{1 + tan 60° tan 30°}}1 + tan 60° tan 30°tan 60° - tan 30°
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Solving,
⇒tan x=tan 60° - tan 30°1 + tan 60° tan 30°⇒tan x=3−131+3×13⇒tan x=3−131+1⇒tan x=232⇒tan x=13⇒tan x=tan 30°⇒x=30°.\Rightarrow \text{tan x} = \dfrac{\text{tan 60° - tan 30°}}{\text{1 + tan 60° tan 30°}} \\[1em] \Rightarrow \text{tan x} = \dfrac{\sqrt{3} - \dfrac{1}{\sqrt{3}}}{1 + \sqrt{3} \times \dfrac{1}{\sqrt{3}}} \\[1em] \Rightarrow \text{tan x} = \dfrac{\dfrac{3 - 1}{\sqrt{3}}}{1 + 1} \\[1em] \Rightarrow \text{tan x} = \dfrac{\dfrac{2}{\sqrt{3}}}{2} \\[1em] \Rightarrow \text{tan x} = \dfrac{1}{\sqrt{3}} \\[1em] \Rightarrow \text{tan x} = \text{tan 30°} \\[1em] \Rightarrow x = 30°.⇒tan x=1 + tan 60° tan 30°tan 60° - tan 30°⇒tan x=1+3×313−31⇒tan x=1+133−1⇒tan x=232⇒tan x=31⇒tan x=tan 30°⇒x=30°.
Hence, x = 30°.
Answered By
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sin x = sin 60° cos 30° + cos 60° sin 30°
cos x = cos 60° cos 30° - sin 60° sin 30°
sin 3x = 2 sin 30° cos 30°
cos(2x - 6°) = cos2 30° - cos2 60°
