Advertisements
Advertisements
Question
Prove that `sqrt((1 + cos "A")/(1 - cos"A"))` = cosec A + cot A
Solution
L.H.S = `sqrt((1 + cos "A")/(1 - cos"A"))`
= `sqrt((1 + cos "A")/(1 - cos "A") xx (1 + cos "A")/(1 + cos "A"))` ......[On rationalising the denominator]
= `sqrt((1 + cos "A")^2/(1 - cos^2 "A"))`
= `sqrt((1 + cos "A")^2/(sin^2 "A")` ......`[(because sin^2"A" + cos^2"A" = 1),(therefore 1 - cos^2"A" = sin^2"A")]`
= `(1 + cos"A")/"sin A"`
= `1/"sin A" + "cos A"/"sin A"`
= cosec A + cot A
= R.H.S
∴ `sqrt((1 + cos "A")/(1 - cos"A"))` = cosec A + cot A
APPEARS IN
RELATED QUESTIONS
Prove that `cosA/(1+sinA) + tan A = secA`
Prove the following trigonometric identities
`((1 + sin theta)^2 + (1 + sin theta)^2)/(2cos^2 theta) = (1 + sin^2 theta)/(1 - sin^2 theta)`
Prove the following trigonometric identities.
`(1 + cot A + tan A)(sin A - cos A) = sec A/(cosec^2 A) - (cosec A)/sec^2 A = sin A tan A - cos A cot A`
Prove the following trigonometric identities.
`(tan A + tan B)/(cot A + cot B) = tan A tan B`
Prove that: `sqrt((sec theta - 1)/(sec theta + 1)) + sqrt((sec theta + 1)/(sec theta - 1)) = 2 cosec theta`
Prove the following identities:
`((1 + tan^2A)cotA)/(cosec^2A) = tan A`
`(tan theta)/((sec theta -1))+(tan theta)/((sec theta +1)) = 2 sec theta`
If m = ` ( cos theta - sin theta ) and n = ( cos theta + sin theta ) "then show that" sqrt(m/n) + sqrt(n/m) = 2/sqrt(1-tan^2 theta)`.
If tan A =` 5/12` , find the value of (sin A+ cos A) sec A.
Write True' or False' and justify your answer the following :
The value of the expression \[\sin {80}^° - \cos {80}^°\]
sec4 A − sec2 A is equal to
If m = a secA + b tanA and n = a tanA + b secA , prove that m2 - n2 = a2 - b2
Find the value of x , if `cosx = cos60^circ cos30^circ - sin60^circ sin30^circ`
Prove that `(tan^2"A")/(tan^2 "A"-1) + (cosec^2"A")/(sec^2"A"-cosec^2"A") = (1)/(1-2 co^2 "A")`
Prove that : `(sin(90° - θ) tan(90° - θ) sec (90° - θ))/(cosec θ. cos θ. cot θ) = 1`
Prove that sin θ sin( 90° - θ) - cos θ cos( 90° - θ) = 0
Prove that: `1/(cosec"A" - cot"A") - 1/sin"A" = 1/sin"A" - 1/(cosec"A" + cot"A")`
Prove that `"cosec" θ xx sqrt(1 - cos^2theta)` = 1
If tan θ × A = sin θ, then A = ?
Prove that
`(cot "A" + "cosec A" - 1)/(cot"A" - "cosec A" + 1) = (1 + cos "A")/"sin A"`
