2007-11-23 19:14:45 · 3 answers · asked by tobi 1 in Science & Mathematics ➔ Mathematics
(csc θ - cot θ)²
= (1/sin θ - cos θ / sin θ)²
= (1 - cos θ)² / sin² θ
= (1 - cos θ)² / (1 - cos² θ)
= (1 - cos θ)² / (1 - cos θ)(1 + cos θ)
= (1 - cos θ) / ( 1 + cos θ)
2007-11-23 19:21:56 · answer #1 · answered by Madhukar 7 · 2⤊ 1⤋
LHS
(1/sin θ - cos θ / sin θ) ²
[(1 - cos θ) / sin θ ] ²
(1 - cos θ)(1 - cos θ) / sin ² θ
(1 - cos θ)(1 - cos θ) / (1 - cos ² θ)
(1 - cos θ)(1 - cos θ) / (1 - cos θ)(1 + cos θ)
(1 - cos θ) / (1 + cos θ)
RHS
(1 - cos θ) / (1 + cos θ )
LHS = RHS
2007-11-23 20:41:11 · answer #2 · answered by Como 7 · 1⤊ 1⤋
RHS = (1-- cos x)/(1 + cos x)
= (1 -- cos x)^2 / (1 + cos x)(1 -- cos x)
= (1 -- cos x)^2 / (1 -- cos^2x)
= (1 -- cos x)^2 / sin^2x
=(1/sinx -- cosx/sinx)^2
= (cosec x -- cot x)^2
= LHS
2007-11-23 21:52:48 · answer #3 · answered by sv 7 · 0⤊ 1⤋