Solve : sin70∘−cos40∘
sin70∘−cos40∘=sin70∘−cos(90∘−50∘)=sin70∘−sin50∘=2sin(70∘−50∘2)cos(70∘+50∘2)=2sin10∘cos60∘=2sin10∘⋅1/2=sin10∘
Prove that:
(i) tan 20o tan 35o tan 45o tan 55o tan 70o=1
(ii) sin 48o sec42o+cos 48o cosec 42o=2
(iii) sin 70ocos 20o+cosec 20osec 70o−2 cos 70o cosec 20o=0
(iv) cos 80osin 10o+cos 59o cosec 31o=2
cos40∘+cos80∘+cos160∘+cos240∘=