Evaluate the following: `sin 36^0cos9^0+cos36^0 sin9^0`

Evaluate the following: sin 78^0cos 18^0-cos 78^0sin 18^0

Evaluate the following: cos 80^0cos 20^0+ sin 80^0 sin 20^0

Evaluate the following: (i) sin39^0-cos51^0 (ii) cos e c25^0-sec65^0 +cot34^0-tan56^0 (iii) (sin36^0)/(cos54^0)-(sin54^0)/(cos36^0) +cos^2 13^0-sin^2 77^0

Evaluate the following: cos 47^0cos 13^0-sin 47^0 sin 13^0

Evaluate the following: (cos37^0)/(sin53^0) (ii) (tan54^0)/(cot36^0) (iv) (cos e c34^0)/(sec56^0)

Find the values of the following: sin75^0 (ii) cos75^0 (iii) sin15^0 (iv) cos15^0

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

Without using trigonometric tables, evaluate each of the following: (sin^2 20^0+sin^2 70^0)/(cos^2 20^0+cos^2 70^0)+(sin(90^0-theta)sintheta)/(tantheta)+(cos(90^0-theta)costheta)/(cottheta)

Evaluate each of the following: (a) cos(40^0-theta)-sin(50^0+theta)+(cos^2 40^0+cos^2 50^0)/(sin^2 40^0+sin^2 50^0) (b) (cos70^0)/(sin20^0)+(cos55^0cos e c35^0)/(tan5^0tan25^0tan45^0tan65^0tan85^0) (c) 2((cos58^0)/(sin32^0))-sqrt(3)((cos38^0cos e c52^0)/(tan15^0tan60^0t a n75^0))

Find the value of x in each of the following: (i) tan3x=sin45^0cos45^0+sin30^0 , (ii) cosx=cos60^0cos30^0+sin60^0sin30^0 , (iii) sin2x=sin60^0cos30^0-cos60^0sin30^0dot