prove the identity of tan times csc = sec?

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prove the identity of tan times csc = sec?

2007-04-02 06:41:23 · 3 answers · asked by Jay w 1 in Science & Mathematics ➔ Mathematics

3 answers

Just convert it all into terms of sin and cos.

tan = sin/cos
csc = 1/sin
sec = 1/cos

So the equation is really:
(sin/cos) * (1/sin) = (1/cos)

Cancel out the sines and you get:
(1/cos) = (1/cos)
... and you're done!

2007-04-02 06:45:51 · answer #1 · answered by Bramblyspam 7 · 0⤊ 0⤋

Recall:
tan = sin / cos
csc = 1/sin
sec = 1/cos

tan * csc = (sin/cos)*(1/sin) = 1 / cos = sec

2007-04-02 06:46:11 · answer #2 · answered by peateargryfin 5 · 0⤊ 0⤋

this is easy..
to prove tan csc = sec,
LHS
= tan csc
= sin/cos * 1/sin (cancel sin)
= 1/cos
= sec
=RHS (proven)

2007-04-02 07:00:26 · answer #3 · answered by gh0st 1 · 0⤊ 0⤋