To prove : cos−145+cos−11213=cos−13365
We use cos(a+b) formula
Let a=cos−145⇒cosa=45
⇒sina=√1−cos2a
=√1−(45)2=√925=35
Let b=cos−11213⇒cosb=1213
⇒sinb=√1−cos2b
=√1−(1213)2=√25169=513
∴sina=35 and sinb=513
∴cosa=45 and cosb=1213
cos(a+b)=cosacosb−sinasinb
cos(a+b)=45×1213−35×513
=4865−313=48−1565
⇒cos(a+b)=3365
⇒a+b=cos−1(3365)
⇒cos−145+cos−11213=cos−13365
Hence proved.