Question

In fig. 8.19 write tan 50$°$, sec 40$°$, sin 50$°$, cos 60$°$, cot 60$°$, cosec 40$°$, cos 30$°$

Answer 1

$$\begin{gathered} \mathrm{In}△\mathrm{LTM},\mathrm{we}\mathrm{have}: \\ \angle \mathrm{MLT}+\angle \mathrm{LMT}+\angle \mathrm{LTM}=180°(\mathrm{Angle}\mathrm{sum}\mathrm{property}) \\ \Rightarrow \angle \mathrm{MLT}+50°+90°=180° \\ \Rightarrow \angle \mathrm{MLT}=40° \\ \mathrm{Similarly},\mathrm{in}△\mathrm{LNT},\mathrm{we}\mathrm{have}: \\ \angle \mathrm{LTN}+\angle \mathrm{TLN}+\angle \mathrm{LNT}=180°(\mathrm{Angle}\mathrm{sum}\mathrm{property}) \\ \Rightarrow 90°+30°+\angle \mathrm{LNT}=180° \\ \Rightarrow \angle \mathrm{LNT}=60° \end{gathered}$$

$$\begin{gathered} \mathrm{Now},\mathrm{we}\mathrm{get}\mathrm{the}\mathrm{following}: \\ \tan 50°=\frac{\mathrm{LT}}{\mathrm{MT}} \\ \sec 40°=\frac{\mathrm{LM}}{\mathrm{LT}} \\ \sin 50°=\frac{\mathrm{LT}}{\mathrm{LM}} \\ \cos 60°=\frac{\mathrm{TN}}{\mathrm{LN}} \\ \cot 60°=\frac{\mathrm{TN}}{\mathrm{LT}} \\ \mathrm{cosec}40°=\frac{\mathrm{LM}}{\mathrm{MT}} \\ \cot 30°=\frac{\mathrm{LT}}{\mathrm{LN}} \end{gathered}$$