`sin^2 4 5^(@)-c o s e c^2 6 0^(@)+sec^2 3 0^(@)`

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^@ )

int(sec^2x)/(c o s e c^2x)dx

Evaluate the following expressions: (i) 2sin^2 30^otan60^o-3cos^2 60^osec^2 30^o (ii) "c o s e c"^2 30^osin^2 45^o-sec^2 60^o (iii) tan60^ocos e c^2 45^o + sec^2 60^otan45^o

Evaluate the following expressions: 2sin^2 30otan60o-3cos^2 60osec^2 30o (ii) "c o s e c"^2 30osin^2 45o-sec^2 60o (iii) tan60ocos e c^2 45o+sec^2 60otan45o

Prove that: (sin70^@)/(cos20^@)+(cos e c\ 20^@)/(sec70^@)-2cos70^@\ cos e c\ 20^@=0

2sin^2(pi/6 )+c o s e c^2((7pi)/6)cos^2(pi/3)=3/2

2sin^2(pi/6 )+c o s e c^2((7pi)/6)cos^2(pi/3)=3/2

Without using trigonometric tables, evaluate each of the following: (sec^2 54^0-cot^2 36^0)/(cos e c^2 57^0-tan^2 33^0)+2sin^2 38^0sec^2 52^0-sin^2 45^0

Find the principal values of " (1) c o s e c"^(-1)(2) and "c o s e c"^(-1)(-2/(sqrt(3)))