Question

Evaluate :$\cos 48°$$-\sin 42°$

Answer 1

Evaluate $\cos 48°$$-\sin 42°$:

To simplify this, convert the $\cos$function into $\sin$ function.

We know that

$48°$can be written as

$48°=90°–42°$

So,

$\cos 48°$$=\cos (90°–42°)$

$\cos (90°–42°)=\sin 42°$ $[\because c\mathrm{os}(90°-\mathrm{\theta })=s\mathrm{in}\mathrm{\theta }]$

Substitute the value, to simplify this equation

$\cos 48°–\sin 42°=\cos (90°–42°)–\sin 42°$

$=\sin 42°–\sin 42°$

$=\sin 42°–\sin 42°$

Thus, The value of $\cos 48°–\sin 42°=0$