Question

$\mathrm{Find}\mathrm{the}\mathrm{value}\mathrm{of}\sin 48°\sec 42°+\cos 48°\mathrm{cosec}42°.$

Answer 1

$$\begin{gathered} \sin 48°\sec 42°+\cos 48°\mathrm{cosec}42° \\ =\sin 48°\mathrm{cosec}\left(90°-42°\right)+\cos 48°\sec \left(90°-42°\right) \\ =\sin 48°\mathrm{cosec}48°+\cos 48°\sec 48° \\ =\sin 48°\times \frac{1}{\sin 48°}+\cos 48°\times \frac{1}{\cos 48°} \\ =1+1 \\ =2 \end{gathered}$$