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Old 01-20-2009   #2
MAS1

 
Join Date: Dec 2008
Posts: 249
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1. 1 - sin/csc = cos/sec

Let's work on the left-hand side (LHS).

1 - sin/(1/sin) = cos/sec

1 - sin*sin = cos/sec

cos*cos = cos/sec

cos(1/sec) = cos/sec

cos/sec = cos/sec


2. 1/(sec*sec) = 1 - 1/(csc*csc)

Work on the RHS.

1/(sec*sec) = 1 - 1/((1/sin)(1/sin))

1/(sec*sec) = 1 - sin*sin

1/(sec*sec) = cos*cos

1/(sec*sec) = (1/sec)(1/sec)

1/(sec*sec) = 1/(sec*sec)
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