Expert: Ahmed Salami - 4/1/2009

Question
I am trying to verify the following identity but don't know where to get
started...... The question is...     (1-sin t)squared/cos t = 1-sin t / 1+ sin t    
could you please help out.  Thanks!   - Willow

Answer
Hi Willow,
I think you meant to prove that
[(1-sin t)/cos t]^2 = 1-sin t / 1+sin t    
Consider the left hand side,
[(1-sin t)/cos t]^2
= (1-sin t)^2/(cos t)^2
but,
(sin t)^2 + (cos t)^2 = 1      (an identity)
and so,
(1-sin t)^2/(cos t)^2
= (1-sin t)^2 / [1 - (sin t)^2]
= (1-sin t)^2 / (1-sin t)(1+sin t)
= 1-sin t / 1+sin t

Hope it helps.

Regards