`(5cos^(6)60^(@)+4sec^(2)30^(@)-tan^(2)45^(@))/(sin^(2)30^(@)+cos^(2)30^(@))`

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^@ )

Evaluate : (tan45^(@))/(2sin30^(@)-cos60^(@))

Evaluate : (sin^(2)30^(@)+sin^(2)45^(@)-4cot^(2)60^(@))/(2sin30^(@)cos30^(@)+(1)/(2)tan60^(@))

Evaluate : (i) sin^(2)30^(@)-2cos^(3)60^(@)+3tan^(4)45^(@) (ii) (cos0^(@)+sin45^(@)+sin30^(@))(sin90^(@)-cos45^(@)+cos60^(@))

Prove that : cos^(2)30^(@)-sin^(2)30^(@)=cos60^(@)

Prove that : cos^(2)30^(@)-sin^(2)30^(@)=cos60^(@)

Verify that cos 60^(@)=(1-tan^(2)30^(@))/(1+tan^(2)30^(@))

Prove that : (i) sin 60^(@) = 2 sin 30^(@) cos 30^(@) (ii) 4(sin^(4) 30^(@) + cos^(4) 60^(@)) - 3(cos^(2)45 - sin^(2)90^(@)) = 2

using trigonometric tables evaluate the following : (cot 30^(@))/(sec 30^(@)) + ("cosec 30"^(@))/(tan 45^(@)) - (2 cos 0^(@))/(sin 30^(@)) + cos^(2) 45^(@)

Show that : 2tan^(2)60^(@)-6(sin^(2)45^(@)-tan^(2)30^(@))=5