5. Prove: cos2 30 ° + sin2 30 ° = 1.

Prove that sin^2 30^@ + cos^2 30^@=1

Prove that sin 30 ^(@) = (1)/(2) .

(sin ^ (2) 30 ^ (@) - cos ^ (2) 30 ^ (@)) / (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 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^@ )

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

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

Prove that cos (30^(@) -A ) cos (30^(@) + A ) + cos (45^(@) - A) cos (45^(@) + A) = cos 2A + (1)/(4) .

Prove that sin^2(30°) + cos^2(60°) - tan^2(45°) = -1/2

Verify that: (i) cos60^@=cos^2 30^@-sin^2 30^@=1/2