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Question Number 68446 by 9102176137086 last updated on 10/Sep/19

cos (x−60)+cos (x−30)=sin x  prove

$$\mathrm{cos}\:\left({x}−\mathrm{60}\right)+\mathrm{cos}\:\left({x}−\mathrm{30}\right)=\mathrm{sin}\:{x} \\ $$$${prove} \\ $$

Commented by mr W last updated on 10/Sep/19

not true!  for x=30°:  cos (30−60)+cos (30−30)  =cos 30+1  =((√3)/2)+1  but sin 30=(1/2)  ⇒LHS≠RHS

$${not}\:{true}! \\ $$$${for}\:{x}=\mathrm{30}°: \\ $$$$\mathrm{cos}\:\left(\mathrm{30}−\mathrm{60}\right)+\mathrm{cos}\:\left(\mathrm{30}−\mathrm{30}\right) \\ $$$$=\mathrm{cos}\:\mathrm{30}+\mathrm{1} \\ $$$$=\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}+\mathrm{1} \\ $$$${but}\:\mathrm{sin}\:\mathrm{30}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\Rightarrow{LHS}\neq{RHS} \\ $$

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