`(5 cos² 60 + 4 sec² 30 - tan² 45) / (sin² 30 + cos² 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^@ )

Verify that : sin 60^@ = 2 sin 30^@ cos 30^@

Evaluate: (cos45)/(sec30+cosec30)

Evaluate the following: 4(sin^4 60o+cos^4 30o)-3(tan^2 60o-tan^2 45o)+5cos^2 45o (ii) (cos e c^2 45osec^2 30o)(sin^2 30o+4cot^2 45o-sec^2 60o)

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

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

Evaluate : [{:(,4 sin 30^@ 2 cos 60^@), (,sin 90^@ 2 cos 0^@):}] [{:(,4,5),(,5,4):}]

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

Find the value of : (i) (tan 45^(@))/("cosec 30"^(@)) + (sec 60^(@))/(cot 45^(@)) - (5 sin 90^(@))/(2 cos 0^(@)) (ii) 3 sin^(2)30^(@) + 2 tan^(2)60^(@) - 5 cot^(2)45

Find the value of x, if : cos x = cos 60^(@) cos 30^(@) + sin 60^(@) sin 30^(@)