Prove the following trigonometric identities:
1−cos A1+cos A=(cot A−cosec A)2
LHS=1−cosA1+cosA
Rationalize the numerator and denominator with (1 – cos A)
=(1−cosA)(1−cosA)(1+cosA)(1−cosA)
=(1−cosA)21−cos2A
=(1−cosA)2sin2A
=(1−cosAsinA)2
=(1sinA−cosAsinA)2
=(cosecA−cotA)2
=(cotA−cosecA)2
=RHS