Question

verify each identity using trig. identities.

1. secxcotx = cscx
2. (1-cos^2x) csc^2=1
3. (1 + tan^2x) sin^2x = tan^2x
4. sinxcosx / (1 +cosx) (1- cosx) = cotx
5. cotx - cosx = cotx (1 - sinx)

Answer 1

\[\sec x \cot x=\frac{ 1 }{ \cos x }\times \frac{ 1 }{ \tan x }=\frac{ 1 }{ \cos x }\times \frac{ \cos x }{ \sin x }=\frac{ 1 }{ \sin x }=\csc x\]

Answer 2

right?

Answer 3

ahh o yes :D

Answer 4

trying

Answer 5

for the second
its rule
\[1-\cos ^{2}x=\sin ^{2}x\]

Answer 6

then
\[\sin ^{2}x \times \csc ^{2}x =1\]

Answer 7

done
right?

Answer 8

(sin^2x)(csc^2x) is equal to 1?

Answer 9

yeah because the cscx=1/sinx

Answer 10

for the third one
its rule
\[1+\tan ^{2}x=\sec ^{2}x\]

Answer 11

\[\sec ^{2}x \times \sin ^{2}x=\frac{ 1 }{ \cos ^{2}x }\times \sin ^{2}x=\tan ^{2}x\]

Answer 12

5
\[\cot x-\cos x=\frac{ \cos x }{ \sin x }-\cos x=\cos x(\frac{ 1 }{ \sin x }-1)=\cos x(\frac{ 1-\sin x }{ \sin x })=\cot x(1-\sin x)\]

Answer 13

4 first
\[\left( 1+\cos x \times \left( 1-\cos x \right) \right)=1-\cos ^{2}x\]

Answer 14

then
\[ 1-\cos ^{2}x=\sin ^{2}x\]

Answer 15

\[\frac{ sinxcosx }{ \sin ^{2}x }=\frac{ cosx }{ sinx }=\cot x\]

Answer 16

done
clear?