Simplify `(sin^(2)2020+cos^(2)2020+tan50)/(sec^(2)2019-tan^(2)2019+cot40)`

Prove :sin^(2)A cot^(2)A+cos^(2)A tan^(2)A=1

(sec^2A)/(cos^2A)-(tan^2A)/(cot^2A)=1+2tan^2A

tan^(2)A+cot^(2)A=sec^(2)A cos ec^(2)A-2

sin ^ (2) A.cot ^ (2) A-cos ^ (2) A * tan ^ (2) A = 1

Prove that (sec^(2)A)/(cos^(2)A)-(tan^(2)A)/(cot^(2)A)=1+2tan^(2)A

The expression cosec^(2)A cot^(2)A-sec^(2)A tan^(2)A-(cot^(2)A-tan^(2)A)(sec^(2)A cosec^(2)A-1) is equal to

Simplify tan^(-1)((cos(x/2)+sin(x/2))/(cos(x/2)-sin(x/2)))

cos ec^(2)A cot^(2)A-sec^(2)A tan^(2)A-(cot^(2)A-tan^(2)A)(sec^(2)A cos ec^(2)A-1)

(sin A+cosec A)^(2)+(cos A+sec A)^(2)=7+tan^(2)A+cot^(2)A

Evaluate : (sec^(2)theta-cot^(2)(90^(@)-theta))/("cosec"^(2)67^(@)-tan^(2)23^(2))+(sin^(2)40^(@)+sin^(2)50^(@))