Question

tan ( pi/2- theta) tan theta=1

Answer 1

ok.. .thanks for sharing that

Answer 2

thank you they're asking to verify the identity.

Answer 3

notice -> http://www.gradeamathhelp.com/image-files/trigonometric-identities-pythagorean.gif <--- the 1st pythagorean identity there

Answer 4

ahemm rather the 2nd one listed there

Answer 5

ohh smokes... .wait a sec... I got the wrong set

Answer 6

http://1.bp.blogspot.com/-57vrQkzCnVA/TxfkOuTBs6I/AAAAAAAABWU/R91jwBewUyE/s1600/cofunction+identities.png <--- there rather, we'll use the 3rd one listed there, from the trig cofunctions

Answer 7

is this how the answer should be Cot theta tan theta=1
cos theta / sin theta times sin theta / cos theta=1
1=1

Answer 8

well... .kinda.. one sec

Answer 9

sure

Answer 10

\(\bf {\color{brown}{ tan\left(\frac{\pi}{2}-\theta\right)}}=cot(\theta)\qquad {\color{olive}{ cot(\theta)}}=\cfrac{cos(\theta)}{sin(\theta)}
\\ \quad \\ \quad \\


tan\left(\frac{\pi}{2}-\theta\right)tan(\theta)=1\implies {\color{brown}{ cot(\theta)}}tan(\theta)=1
\\ \quad \\
{\color{olive}{ \cfrac{\cancel{ cos(\theta) }}{\cancel{ sin(\theta) }}}}
\cdot
\cfrac{\cancel{ sin(\theta) }}{\cancel{ cos(\theta) }}=1\)

Answer 11

wht is tht ?

Answer 12

hmmm anything you find confusing? there's an assumption you know trig btw

Answer 13

if you are a beginner,then
\[\tan \left( \frac{ \pi }{ 2 } - \theta \right)=\frac{ \sin \left( \frac{ \pi }{ 2}-\theta \right) }{ \cos \left( \frac{ \pi }{ 2 } -\theta \right) }\]
\[=\frac{ \sin \frac{ \pi }{ 2 }\cos \theta-\cos \frac{ \pi }{ 2} \sin \theta }{ \cos \frac{ \pi }{ 2 }\cos \theta+\sin \frac{ \pi }{ 2 } \sin \theta }\]
\[(\sin \frac{ \pi }{ 2 }=1,\cos \frac{ \pi }{ 2 }=0)\]
\[=\frac{ \cos \theta }{ \sin \theta }\]