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

Evaluate : sin 75^@, cos 75^@, tan 75^@ .

Evaluate : sin 15^@, cos 15^@, tan 15^@ .

Simplify the following : (cos (360^@-theta) cosec (180^@+ theta) cot (90^@-theta))/(sec (90^@+theta)cos (-theta)) .

Prove that : cosec 60^@ cot 30^@ tan 60^@= 2 sec^2 45^@ cos30^@ .

Simplify the following : sin(90^@+ theta) tan (270^@ +theta) cot (90^@+theta) cosec (270^@+theta) .

Evaluate The following : (sin 30^@+ tan 45^@ - cosec 60^@)/(sec 30^@+cos 60^@ + cot 45^@)

Evaluate :- (5sin^2 30^@+cos^2 45^@+4tan^2 45^@)/(2sin30^@ cos60^@+tan45^@) .

Prove that : ((sin 0^@+ cos30^@)(sin30^@+tan45^@))/((tan 30^@+ cot 60^@)(sec 60^@-cosec90^@))=9/8 .

Solve the 2 tan^-1 (cos x) = tan^-1 (2 cosec x) .