SOLUTION: VERIFY each trigonometric identity: I'd appreciate any help:) a) (1/cos^2x)-(1/cot^2x)=1 b) (sinx/1+cosx)=(1-cosx/sinx) c) (secx/sinx)-(sinx/cosx)=cotx d) (cos^2x/1-sinx)=si

Question 446108: VERIFY each trigonometric identity:
I'd appreciate any help:)
a) (1/cos^2x)-(1/cot^2x)=1
b) (sinx/1+cosx)=(1-cosx/sinx)
c) (secx/sinx)-(sinx/cosx)=cotx
d) (cos^2x/1-sinx)=sinx+1
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
VERIFY each trigonometric identity:
I'd appreciate any help:)
a) (1/cos^2x)-(1/cot^2x)=1
----
Multiply thru by cot^2 to get:
[cos^2/sin^2][1/cos^2) - 1 = cot^2
Cancel the cos^2:
1/sin^2 - 1 = cot^2
csc^2-1 = cot^2
cot^2 = cot^2
===========================
b) (sinx/1+cosx)=(1-cosx/sinx)
Cross-multiply:
sin^2 = (1+cos)(1-cos)
sin^2 = 1-cos^2
sin^2 = sin^2
============================
c) (secx/sinx)-(sinx/cosx)=cotx
Multiply thru by sincos to get:
(cos*sec) - sin^2 = cos^2
1-sin^2 = cos^2
cos^2 = cos^2
=============================
d) (cos^2x/1-sinx)=sinx+1
Multiply both sides by 1-sin to the:
cos^2 = (1-sin)(1+sin)
cos^2 = 1-sin^2
cos^2 = cos^2
============================
Cheers,
Stan H.

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