`(1) (sin1 8^@)/(cos7 2^@) (i i)(tan2 6^@)/(cot6 4^@)`

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

The value of sin^(-1)(sin5)+cos^(-1)(cos 10)+ tan^(-1)(tan (-6))+cot^(-1)(cot(-10)) is a) 8pi - 21 b) 6pi - 19 c) 9+4pi d)None of these

The value of sin^(-1)(cos2)-cos^(-1)(sin2)+tan^(-1)(cot4)-cot^(-1)(tan4)+sec^(-1)(cos ec6)-cos ec^(-1)(sec6

The value of sin^(-1)(cos2)-cos^(-1)(sin2)+tan^(-1)(cot4)-cot^(-1)(tan4)+sec^(-1)(cosec6)-cosec^(-1)(sec6) is

(sec 8 A-1)/( sec 4A-1)= ..................... A) (tan 2A)/( tan 8A) B) (tan 8A)/(tan 2A) C) (cot 8A)/(cot 2A) D) (tan 6A)/(tan 2A)

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 (i) (sec 8A -1)/(sec 4A -1) =(tan 8A)/(tan 2A) (ii) (cos A+ sin A)/(cos A - sin A)-(cos A-sin A)/(cos A+sin A)=2 tan 2A

Show that (i) sin^(8)A-cos^(8)A=(sin^(2)A-cos^(2)A)(1-2sin^(2)A.cos^(2)A) (ii) (1)/(sec A-tan A)-(1)/(cos A)=(1)/(cos A)-(1)/(sec A + tan A)

Show that (i) sin^(8)A-cos^(8)A=(sin^(2)A-cos^(2)A)(1-2sin^(2)A.cos^(2)A) (ii) (1)/(sec A-tan A)-(1)/(cos A)=(1)/(cos A)-(1)/(sec A + tan A)

Show that sin ^ (- 1) ((sin (3 pi)) / (7)) + cos ^ (- 1) ((cos (46 pi)) / (7)) + tan ^ (- 1) (- (tan (13 pi)) / (8)) + cot ^ (- 1) (cot (- (19 pi) / (8))) = (13 pi) / (7)