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^@ ) `

Explanation

(i) `sin60^@cos30^@ + sin30^@cos60^@`

`=sin(60^@+30^@) = sin90^@ = 1`




(ii)`2tan^2 45^@ +cos^2 30^@ - sin^2 60^@`

`=2(1)^2 +(sqrt3/2)^2 - (sqrt3/2)^2`

`=2`



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