`sin 690^@ cos 930^@ + tan(-765^@) cosec (-1170^@)`

sin 300^@ cosec 1050^@ - tan (-120^@)

Evaluate : (sin 35^(@) cos 55^(@) + cos 35^(@) sin 55^(@))/ (cosec^(2) 10^(@) - tan^(2) 80^(@))

Find x, if : sin 47 ^(@) sec 43 ^(@) + cos 43 ^(@) cosec 47 ^(@) - x cos ^(2) 45 ^(@) = 0.

Prove that : tan 225^@ cot 405^@+ tan 765^@ cot 675^@=0

Evaluate cos 40 ^(@) cosec 50 ^(@)+ sin 50 ^(@) sec 40 ^(@)

Show that : sin A cos A - (sin A cos(90^(@) - A) cos A)/ (sec (90^(@) - A)) - (cos A sin (90^(@) - A) sin A)/ (cosec (90^(@) - A)) = 0

2 tan^(-1) (cos x) = tan^(-1) (2 cosec x)

Show that : (i) tan 10^(@) tan 15^(@) tan 75^(@) tan 80^(@) = 1 (ii) sin 42^(@) sec 48^(@) + cos 42^(@) "cosec 48"^(@) = 2

Prove that: (i) cos55^(@)sin 35^(@)+sin 55^(@)cos 35^(@)=1 (ii) (tan 72^(@))/(cot 18^(@))-(cot 72^(@))/(tan18^(@))=0 (iii) sec70^(@)sin 20^(@)+cosec 70^(@)cos 20^(@)=2

Evaluate : (i) cosec 82^(@)-sec8^(@) (ii) sec 70^(@)sin 20^(@)+cos 20^(@)cosec 70^(@)