Advertisements
Advertisements
Question
Prove the following identity :
`cosecA + cotA = 1/(cosecA - cotA)`
Advertisements
Solution
LHS = cosecA + cotA
= `(cosecA + cotA)/1 . (cosecA - cotA)/(cosecA - cotA)`
= `(cosec^2A - cot^2A)/(cosecA - cotA) = (1 + cot^2A - cot^2A)/(cosecA - cotA)`
= `1/(cosecA - cotA)`
APPEARS IN
RELATED QUESTIONS
If secθ + tanθ = p, show that `(p^{2}-1)/(p^{2}+1)=\sin \theta`
Prove the following trigonometric identities.
`(tan^3 theta)/(1 + tan^2 theta) + (cot^3 theta)/(1 + cot^2 theta) = sec theta cosec theta - 2 sin theta cos theta`
Prove that `sqrt((1 + cos theta)/(1 - cos theta)) + sqrt((1 - cos theta)/(1 + cos theta)) = 2 cosec theta`
Prove the following identities:
cosec4 A (1 – cos4 A) – 2 cot2 A = 1
If tan A = n tan B and sin A = m sin B, prove that `cos^2A = (m^2 - 1)/(n^2 - 1)`
`1/((1+ sin θ)) + 1/((1 - sin θ)) = 2 sec^2 θ`
If `sin theta = x , " write the value of cot "theta .`
Prove the following identities.
`sqrt((1 + sin theta)/(1 - sin theta)) + sqrt((1 - sin theta)/(1 + sin theta))` = 2 sec θ
Prove that `(sin θ + tan θ)/(cos θ) = tan θ (1 + sec θ)`.
If cosA + cos2A = 1, then sin2A + sin4A = 1.
