Advertisements
Advertisements
Question
Prove the following identities:
`cosecA + cotA = 1/(cosecA - cotA)`
Advertisements
Solution
L.H.S. = `cosecA + cotA`
= `(cosecA + cotA)/1 xx (cosecA - cotA)/(cosecA - cotA)`
= `(cosec^2A - cot^2A)/(cosecA - cotA)`
= `(1 + cot^2A - cot^2A)/(cosecA - cotA)`
= `1/(cosecA - cotA)` = R.H.S.
APPEARS IN
RELATED QUESTIONS
Prove the following trigonometric identities.
`cot theta - tan theta = (2 cos^2 theta - 1)/(sin theta cos theta)`
If sec A + tan A = p, show that:
`sin A = (p^2 - 1)/(p^2 + 1)`
Prove the following identity :
`(cosecA - sinA)(secA - cosA)(tanA + cotA) = 1`
Prove the following identity :
`sin^4A + cos^4A = 1 - 2sin^2Acos^2A`
Prove the following identity :
`sqrt(cosec^2q - 1) = "cosq cosecq"`
If secθ + tanθ = m , secθ - tanθ = n , prove that mn = 1
Without using trigonometric table , evaluate :
`(sin49^circ/sin41^circ)^2 + (cos41^circ/sin49^circ)^2`
Prove that `"cosec" θ xx sqrt(1 - cos^2θ) = 1`.
Prove that sec2θ – cos2θ = tan2θ + sin2θ.
The value of 2sinθ can be `a + 1/a`, where a is a positive number, and a ≠ 1.
