" (iv) "(sin(90^(@)-A)sin A)/(tan A)-1=-sin^(2)A

Prove that (i) sin (90^(2)-A)cos (90^(@)-A)=(tanA)/(1+tan^(2)A) (ii) (cos(90^(@)-A).cosA)/(cotA)-sin^(2)A=0

Prove the following identities: cos theta sin(90o-theta)+sin theta cos(90o-theta)=1sin(sin(90o-theta))/(tan theta)-1=-sin^(2)theta( iii) (sin(90o-theta)cos(90o-theta))/(tan theta)=1-sin^(2)theta

(sin(90^(@) -theta)sin theta)/(tan theta) + sin^(2) theta is equal to

(tan ^ (2) A sin ^ (2) A) / (tan ^ (2) A-sin ^ (2) A) = 1

Prove that : (1)/ (1 + sin (90^(@) - A)) + (1)/ (1 - sin (90^(@) - A)) = 2 sec^(2) (90^(@) - A)

Show that : sin A cos A - (sin A cos(90^(@) - A) cos A)/ (sec (90^(@) - A)) - (cos A sin (90^(@) - A) sin A)/ (cosec (90^(@) - A)) = 0

(sin^(2) 20^(@) + sin^(2) 70^(@))/(cos^(2) 20^(@) + cos^(2) 70^(@)) + [ (sin (90^(@) - theta).sin theta)/(tan theta) + (cos (90^(@) - theta).cos theta)/(cot theta) ] .

(3 pi)/(2) The value of int_(0)^((3 pi)/(2))(|tan^(-1)tan x|-|sin^(-1)sin x|)/(|tan^(-1)tan x|+|sin^(-1)sin x|)dx is equal to

(cos theta)/(sin(90^(@)+theta))+(sin(-theta))/(sin(180^(@)+theta))-(tan(90^(@)+theta))/(cot theta)