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**MAS1** · 01-20-2009

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)

01-20-2009	#2
MAS1 Join Date: Dec 2008 Posts: 249	1. 1 - sin/csc = cos/sec Let's work on the left-hand side (LHS). 1 - sin/(1/sin) = cos/sec 1 - sinsin = cos/sec coscos = cos/sec cos(1/sec) = cos/sec cos/sec = cos/sec 2. 1/(secsec) = 1 - 1/(csccsc) Work on the RHS. 1/(secsec) = 1 - 1/((1/sin)(1/sin)) 1/(secsec) = 1 - sinsin 1/(secsec) = coscos 1/(secsec) = (1/sec)(1/sec) 1/(secsec) = 1/(secsec)