Advertisements
Advertisements
Question
Prove that:
`cot^2A/(cosecA - 1) - 1 = cosecA`
Solution
`cot^2A/(cosecA - 1) - 1`
= `(cot^2A - cosecA + 1)/(cosecA - 1)`
= `(-cosecA + cosec^2A)/(cosecA - 1)`
= `(cosecA(cosecA - 1))/(cosecA - 1)`
= cosec A
APPEARS IN
RELATED QUESTIONS
`Prove the following trigonometric identities.
`(sec A - tan A)^2 = (1 - sin A)/(1 + sin A)`
Given that:
(1 + cos α) (1 + cos β) (1 + cos γ) = (1 − cos α) (1 − cos α) (1 − cos β) (1 − cos γ)
Show that one of the values of each member of this equality is sin α sin β sin γ
Prove the following identities:
`(costhetacottheta)/(1 + sintheta) = cosectheta - 1`
If x cos A + y sin A = m and x sin A – y cos A = n, then prove that : x2 + y2 = m2 + n2
Prove that:
(sin A + cos A) (sec A + cosec A) = 2 + sec A cosec A
Prove that:
`(sin^2θ)/(cosθ) + cosθ = secθ`
Prove the following identities:
`(tan"A"+tan"B")/(cot"A"+cot"B")=tan"A"tan"B"`
Prove the following identity :
`(sinA - sinB)/(cosA + cosB) + (cosA - cosB)/(sinA + sinB) = 0`
Find x , if `cos(2x - 6) = cos^2 30^circ - cos^2 60^circ`
Prove that:
`sqrt((sectheta - 1)/(sec theta + 1)) + sqrt((sectheta + 1)/(sectheta - 1)) = 2cosectheta`
