Evaluate each of the following: `cot 12^circcot 38^circcot52^circcot60^circcot78^circ` `tan5^circtan25^circtan30^circtan65^circtan85^circ`

Without using trigonometric tables, evaluate each of the following: (sec^2 54^0-cot^2 36^0)/(cos e c^2 57^0-tan^2 33^0)+2sin^2 38^0sec^2 52^0-sin^2 45^0

Evaluate the following: (tan45^@)/(cos e c\ 30^@)+(sec60^@)/(cot45^@)-(5sin90^@)/(2cos0^@)

Evaluate each of the following: (sin60^o)/(cos^2 45^o)-cot30^o + 15cos90^o\ (ii) (5sin^2 30^o + cos^2 45^o-4tan^2 30^o)/(2sin30^ocos30^o + tan45^o)

Without using trigonometric tables, evaluate each of the following: (sec39)/(cosec 51)+2/(sqrt(3))tan17tan38tan60tan52tan73-3(sin^2 31+sin^2 59)

Evaluate each of the following: tan("c o s e c"^(-1)(13)/5) (ii) tan("sec"^(-1)(13)/12) (iii) tan("cot"^(-1)(8)/15)

Evaluate each of the following: (a) cos(40^0-theta)-sin(50^0+theta)+(cos^2 40^0+cos^2 50^0)/(sin^2 40^0+sin^2 50^0) (b) (cos70^0)/(sin20^0)+(cos55^0cos e c35^0)/(tan5^0tan25^0tan45^0tan65^0tan85^0) (c) 2((cos58^0)/(sin32^0))-sqrt(3)((cos38^0cos e c52^0)/(tan15^0tan60^0t a n75^0))

Evaluate the following (i) sin 60^@ cos30^@ + sin 30^@ cos 60^@ (ii) 2tan^2 45^@ + cos^2 30^@ - sin^2 60^@ (iii) (cos45^@)/(sec30^@ + c o s e c 30^@) (iv) (sin30^@ + tan45^@ - c o s e c 60^@ )/(sec30^@ + cos60^@ +cot45^@) (v) (5cos^2 60^@ + 4sec^2 30^@ - tan^2 45^@ )/ (sin^2 30^@ + cos^2 30^@ )

Evaluate the following: (tan^2 60o+4cos^2 45o+3sec^2 30o+5cos^2 90o)/(cos e c\ 30o+sec60o-cot^2 30o)

Evaluate : sin^(2)25^(@)+sin^(2)65^(@)+sqrt(3)tan5^(@)tan15^(@)tan30^(@)tan75^(@)tan85^(@)

Evaluate : 2((cos65^(@))/(sin25^(@)))-(tan20^(@))/(cot70^(@))-sin90^(@)+tan5^(@)tan35^(@)tan60^(@)tan55^(@)tan85^(@)