{ \cot(a) }^(2) ( \sec(a ) - 1 / 1 + \sin(a) ) + \sec {a}^(2) ( \sin(a) - 1 / 1 + \sec(a) ) = 0 prove that ​

Question

`{ \cot(a) }^(2) ( \sec(a ) - 1 / 1 + \sin(a) ) + \sec {a}^(2) ( \sin(a) - 1 / 1 + \sec(a) ) = 0`

prove that


​

Answer 1

in explanation

Explanation:

LHS =1+sinAcot2A(secA−1)

=sin2A(1+sinA)×cosAcos2A(1−cosA)

=sin2A(1+sinA)cosA(1−cosA)×(1−sinA)(1+cosA)(1−sinA)×(1+cosA)

=(1+cosA)(1−sinA)×cosA1

=cosA×cosA(1+secA)1×(1−sinA)

=sec2A(1+secA1−sinA)