Prove the following: `(tan(90^0-A)cotA)/(cos e c^2A)-cos^2A=0`

Prove the following: (tan(90^(@)-A)cot A)/(cos ec^(2)A)-cos^(2)A=0

Prove the following: sin theta sin(90^(@)-theta)-cos theta cos(90^(@)-theta)=0

Prove the following: sin theta sin(90^(@)-theta)-cos theta cos(90^(@)-theta)=0

(tan(90^@-theta) cot theta)/(cosec^2 theta)-cos^2 theta=0

In any triangle ABC, prove that following: (cos^(2)B-cos^(2)C)/(b+c)+(cos^(2)C-cos^(2)A)/(c+a)+(cos^(2)A-cos^(2)B)/(a+b)=0

Without using trigonometric tables, evaluate each of the following: (-tanthetacot(90^0-theta)+secthetacos e c(90^0-theta)+sin^2 35^0+sin^2 55^0)/(tan10^0tan20^0tan30^0tan70^0tan80^0)

In a ABC, prove the following :a(cos B+cos C-1)+b(cos C+cos A-1)+c(cos A+cos B-1)=0

Evaluate the following limit: (lim)_(x->0)(cos2x-cos e c2x)/x

Prove the following : int_(0)^(1)e^(-x)cos^(2)xdx lt int_(0)^(1)e^(-x^(2))cos^(2)xdx

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))