Question

Prove that sin 48° sec 42° + cos 48° cosec 42° = 2

Answer 1

We will simplify the left-hand side

`sin 48° sec 42° + cos 48° cosec 42° = sin 48^@. sec(90^@ - 48^@) + cos 48^@ cosec (90^@ - 48^@)`

`= sin 48^@. sec 48^@ + cos 48^@. cosec 42^@ = sin 48^@ . sec(90^@ - 48^@) + cos 48^@.cosec (90^@ - 48^@)`

`= sin 48^@.cos 48^@ + cos 48^@. sin 48^@`

= 1 + 1

= 2

Proved