Advertisements
Advertisements
Question
Prove that `(cot A)/(1 - cot A) + (tan A)/(1 - tan A) = -1`.
Advertisements
Solution
L.H.S. = `(cot A)/(1 - cot A) + (tan A)/(1 - tan A)`
= `(cot A)/(1 - 1/(tan A)) + (tan A)/(1 - tan A)`
= `(cot A)/((tan A - 1)/(tan A)) + (tan A)/(1 - tan A)`
= `(cot A tan A)/(tan A - 1) + (tan A)/(1 - tan A)`
= `1/(tan A - 1) + (tan A)/(1 - tan A)` ...[∵ cot A tan A = 1]
= `- 1/(1 - tan A) + (tan A)/(1 - tan A)`
= `- (1/(1 - tan A) - (tan A)/(1 - tan A))`
= `-((1 - tan A)/(1 - tan A))`
= –1
= R.H.S.
∴ `(cot A)/(1 - cot A) + (tan A)/(1 - tan A) = -1`
APPEARS IN
RELATED QUESTIONS
Prove the following trigonometric identity.
`cos^2 A + 1/(1 + cot^2 A) = 1`
Prove the following trigonometric identities.
`(1 + sec theta)/sec theta = (sin^2 theta)/(1 - cos theta)`
Prove the following trigonometric identities.
`tan θ/(1 - cot θ) + cot θ/(1 - tan θ) = 1 + tan θ + cot θ`
Prove the following trigonometric identities.
`(1 + cos A)/sin^2 A = 1/(1 - cos A)`
Prove the following trigonometric identities.
`cos A/(1 - tan A) + sin A/(1 - cot A) = sin A + cos A`
Prove the following trigonometric identities.
`(1 - tan^2 A)/(cot^2 A -1) = tan^2 A`
Prove that:
`cosA/(1 + sinA) = secA - tanA`
`sin theta / ((1+costheta))+((1+costheta))/sin theta=2cosectheta`
Write the value of `(1 - cos^2 theta ) cosec^2 theta`.
Write the value of `(sin^2 theta 1/(1+tan^2 theta))`.
If `cos theta = 2/3 , " write the value of" (4+4 tan^2 theta).`
If \[\sin \theta = \frac{1}{3}\] then find the value of 2cot2 θ + 2.
Prove the following identity :
secA(1 - sinA)(secA + tanA) = 1
Prove the following identity :
`((1 + tan^2A)cotA)/(cosec^2A) = tanA`
Prove the following identity :
`sqrt((1 + sinq)/(1 - sinq)) + sqrt((1- sinq)/(1 + sinq))` = 2secq
Prove the following identities.
`costheta/(1 + sintheta)` = sec θ – tan θ
sec 60° = ?
cot θ . tan θ = ?
Prove that cot2θ × sec2θ = cot2θ + 1.
The value of the expression [cosec(75° + θ) – sec(15° – θ) – tan(55° + θ) + cot(35° – θ)] is ______.
