Show that : ` cos15^(@)cos35^(@)"cosec" 55^(@)sin30^(@)"cosec"75^(@)=(1)/(2)`

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

"cosec"(sin^(-1)x+cos^(-1)x)

Evaluate (sin35^(@))/(cos55^(@))+(sec20^(@))/("cosec"70^(@)) .

Evaluate : (cos 45^(@))/(sec30^(@)+"cosec "30^(@))

The value cosec (67^@ + theta) - sec(23^@- theta) + cos15^@ cos35^@ cosec55^@ cos60^@ cosec75^@ is:

Without using trigonometric tables , evaluate : (i) (sin11^(@))/(cos79^(@)) (ii) (sec15^(@))/("cosec"75^(@)) (iii) (tan54^(@))/(cot36^(@)) (iv) (cos68^(@))/(sin22^(@)) (v) ("cosec"24^(@))/(sec66^(@)) (vi) (cot18^(@))/(tan72^(@))

Find the value of (sin 50^(@))/(cos40^(@))+("cosec"40^(@))/(sec 50^(@))-4cos 50^(@) " cosec"40^(@).

The value of (sin25^(@)cos65^(@)+cos25^(@)sin65^(@))/(tan^(2)70^(@)-cosec^(2)20^(@))

Evaulate : 4-(sin30^(@)+tan45^(@)-"cosec"60^(@))/(sec30^(@)+cos60^(@)+cot45^(@))

The value cosec(67^@ +theta)-sec (23^@ -theta)+cos 15^@ cos35^@ cosec 55^@ cos60^@ cosec 75^@ is: cosec(67^@ +theta)-sec (23^@ -theta)+cos 15^@ cos35^@ cosec 55^@ cos60^@ cosec 75^@ का मान है :