Prove that :
`(i) tan 5^@tan 25^@ tan 30^@tan 65^@tan 85^@=(1)/(sqrt(3))`
`(ii) cot 12^@cot38^@cot 52^@cot60^@cot78^@=(1)/(sqrt(3))`
`(iii) cos 15^@cos 35^@cosec 55^@cos 60^@cosec 75^@=(1)/(2)`
`(iv) cos 1^@cos 2^@cos 3^@.....cos 180^@=0`
`(v) ((sin 49^@)/(cos 41^@))^2+ ((cos 41^@)/(sin 49^@))^2=2`

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

((tan35 ^ (@)) / (cot55 ^ (@))) + ((cos78 ^ (@)) / (sin (12 ^ (@)))) - 1

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

Prove that (i) " sin " 75^(@) =((sqrt(6)+sqrt(2)))/(4) (ii) (cos 135^(@) -cos 120^(@))/(cos 135^(@) +cos 120^(@)) =(3 -2sqrt(2)) (iii) " tan " 15^(@) +" cot " 15^(@) =4

Prove that sec 30^(@)tan 60^(@)+sin 45^(@)" cosec "45^(@)+cos30^(@)cot 60^(@)=(7)/(2) .

Without using trigonometric tables, evaluate : (i) (sin16^@)/(cos 74^@) (ii) (sec 11^@)/(cosec 79^@) (iii) (tan 27^@)/(cot 63^@) (iv) (cos 35^@)/(sin 55^@) (v) (cosec 42^@)/(sec 48^@) (vi) (cot 38^@)/(tan 52^@)

Prove that : (i) ((tan 60^(@)+1)/(tan 60^(@) - 1))^(2) = (1 + cos 30^(@))/(1 - cos 30^(@)) (ii) 3 "cosec"^(2) 60^(@) - 2 cot^(2) 30^(@) + sec^(2) 45^(@) = 0

Prove that : (i) (sin 70^@)/(cos 20^@)+(cosec 20^@)/(sec 70^@)-2cos 70^@cosec 20^@=0 (ii) (cos 80^@)/(sin 10^@)+cos 59^@cosec 31^@=2 (iii) (2 sin 68^@)/(cos 22^@)-(2 cot 15^@)/(5 tan 75^@)-(3tan 45^@tan 20^@tan 40^@tan 50^@tan 70^@)/(5)=1 (iv) (sin 18^@)/(cos 72^@)+sqrt(3) (tan 10^@ tan 30^@tan 40^@tan 50^@tan 80^@)=2 (v) (7cos 55^@)/(3 sin 35^@)-(4(cos 70^@cosec 20^@))/(3(tan 5^@tan 25^@tan 45^@tan 65^@tan 856^@))=1