Prove the following trigonometrical identities
`(sin A + cosecA)^2 +(cosA + secA)^2 = tan^2 A + cot^2 A + 7`

Solve the following trigonometric equation : 7 sin^2 x+ 3 cos^2 x=4 .

Solve the following trigonometric equation : cot x + tan x = 2 cosec x .

Solve the following trigonometric equation : cosec^2 theta= 2 cot theta .

Solve the following trigonometric equation : tan theta+ cot theta=2 .

Solve the following trigonometric equation : cot^2 x+ 3/(sin x)+3=0 .

Prove the following identities, where the angles involved are acute angles for which the expressions are defined. : (sin A + cosec A)^2+(cosA+secA)^2=7+tan^2A+cot^2A .

Solve the following trigonometric equation : tan^2 theta+cot^2 theta=2 .

Prove the following identity : sin^2 A cos^2 B + cos^2 A sin^2 B + cos^2 A cos^2 B+ sin^2 A sin^2 B = 1 .

Solve the following trigonometric equation : 2 tan theta-cot theta-1=0 .

Prove the following identity : (1 - tan x)^2+(1 -cot x)^2 = (sec x -cosec x)^2 .