Question

If sin(a+b)= 1 and tan(a-b)=1+root3 then find value of tana + cotb

Answer 1

Dear student,

$$\begin{gathered} \sin (a+b)=1 \\ \Rightarrow (a+\hspace{0.17em}b)=90°---\left(i\right) \\ \tan (a-b)=1+\surd 3 \\ \Rightarrow (a-b)=70°----\left(ii\right) \\ Solving\left(i\right)and\left(ii\right).Weget: \\ a=80°andb=10° \\ \tan \left(a\right)+\hspace{0.17em}cot\left(b\right)=\tan (80°)+cot(10°)=\tan (80°)+\tan (80°)=11.34 \end{gathered}$$

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