Question

if cosec theta minus sin theta is equal to a cube and sec theta minus cos theta is equal to b cube prove that a square b square in bracket a square + b square bracket complete is equal to 1

Answer 1

to prove (a^2)(b^2) ( a^2 + b^2 ) = 1
sin - 1/sin = a^3
(sin^2 - 1)/sin =a^3
cos^2/sin= a^3
cot.cos=a^3
similarly tan.sin=b^3
(a+b)^3= a^3 + b^3 + 3ab(a+b)
cot.cos + sin.tan + 3a^2b + 3ab^2
cos/tan + sin.tan + .....
(cos + sin.tan^2)/tan +....
(cos + sin(sec^2 - 1))/tan +...
(cos + sin.sec^2 -sin)/tan....
through simplification using sin and cos only,
cos^2/sin +1/sin + cos + ...
(cos^2 + 1)/sin + cos + ....
couldn't get beyond this