Evaluate :i) tan 36°/cot 54°ii) cos 12° - sin 78°iii) cosec 31° -

1.	Evaluate :i) tan 36°/cot 54°ii) cos 12° - sin 78°iii) cosec 31° - sec 58°
Answer» HELLO FRIEND!!!!!! QUESTION 1: $\frac{ \tan(36) }{ \cot(54) }$ we know the identity that : $\tan(90 - theeta) = \cot(theeta)$ thus, $\tan(36) = \tan(90 - 36)$ $\tan(36) = \cot(54)$ thus equation becomes: $\frac{ \cot(54) }{ \cot(54) }$ $1$ thus answer of question 1 is 1 question 2 $\cos(12) - \sin(78)$ again using same identity, where theeta is 12 degree.... $\cos(12) = \sin(90 - 12)$ $\cos(12) = \sin(78)$ so equation becomes... $\sin(78) - \sin(78)$ which is 0..... thus answer of question 2 becomes 0 question 3 $\csc(31) - \<klux>SEC</klux>(58)$ using same identity ... $\csc(31) = \csc(90 - 59)$ so here there is an ERROR in question...the question should be sec 59 degree ..... $\sec(58)$ $- \sec(58)$ which is 0 thus answer of corrected question 3 would be 0 .. THANK YOU