প্রমাণ করো :tanA/(1-cotA)+cotA/(1-tanA)=...

প্রমাণ করো :`tanA/(1-cotA)+cotA/(1-tanA)=1+tanA+cotA=1+secAcosecA`

Text Solution

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The correct Answer is:

`tanA/(1-cotA)+cotA/(1-tanA)=tan^2A/(tanA-1)+1/(tanA-tan^2A)`
`=1/(tanA-1)[tan^2A-1/tanA]`
`(tan^3A-1)/((tanA-1).tanA)`
`=(tan^2+tanA+1)/tanA`
`=tanA+cotA+1`
`=secA.cosecA+1`

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The expression tanA(1-cotA)+cotA/(1-tanA) can be written as

secAcosecA+1

tanA+cotA

secA+cosecA

1+sinAcosA

(cotAcosA)/(cotA + cosA) = ?

(cotA + cosA)/(cotAcosA) = ?

(cotAcosA)/(cosA - cotA)

(cotA - cosA)/`(cosecA.cos^2A)` = ?

(cosA - cotA)/(cotAcosA)

If (1+tanA)(1+tanB)=2 , then tan(A+B)=

-1

`(1)/(2)`