Advertisements
Advertisements
Question
Prove the following identities:
`((cosecA - cotA)^2 + 1)/(secA(cosecA - cotA)) = 2cotA`
Advertisements
Solution
L.H.S. = `((cosecA - cotA)^2 + 1)/(secA(cosecA - cotA))`
= `(cosec^2A + cot^2A - 2cosecAcotA + 1)/(secA(cosecA - cotA))`
= `(cosec^2A + (1 + cot^2A) - 2cosecAcotA)/(secA(cosecA - cotA))`
= `(cosec^2A + cosec^2A - 2cosecAcotA)/(secA(cosecA - cotA))`
= `(2cosec^2A - 2cosecAcotA)/(secA(cosecA - cotA))`
= `(2cosecA(cosecA - cotA))/(secA(cosecA - cotA))`
= `(2cosecA)/secA`
= `(2 1/sinA)/(1/cosA)`
= `2/sinA xx cosA/1`
= `2 cosA/sinA`
= 2 cot A = R.H.S.
RELATED QUESTIONS
Prove the following trigonometric identities.
`(tan A + tan B)/(cot A + cot B) = tan A tan B`
Write the value of ` sin^2 theta cos^2 theta (1+ tan^2 theta ) (1+ cot^2 theta).`
If \[\sin \theta = \frac{4}{5}\] what is the value of cotθ + cosecθ?
Prove the following identity :
`(cot^2θ(secθ - 1))/((1 + sinθ)) = sec^2θ((1-sinθ)/(1 + secθ))`
If `(cos alpha)/(cos beta)` = m and `(cos alpha)/(sin beta)` = n, then prove that (m2 + n2) cos2 β = n2
If 1 + sin2α = 3 sinα cosα, then values of cot α are ______.
Given that sinθ + 2cosθ = 1, then prove that 2sinθ – cosθ = 2.
Simplify (1 + tan2θ)(1 – sinθ)(1 + sinθ)
tan θ × `sqrt(1 - sin^2 θ)` is equal to:
If sinθ = `11/61`, then find the value of cosθ using the trigonometric identity.
