Advertisements
Advertisements
Question
Prove that:
`sqrt(sec^2A + cosec^2A) = tanA + cotA`
Advertisements
Solution
L.H.S. = `sqrt(sec^2A + cosec^2A)`
= `sqrt(1/cos^2A + 1/sin^2A)`
= `sqrt((sin^2A + cos^2A)/(sin^2Acos^2A)`
= `sqrt(1/(sin^2Acos^2A)`
= `sqrt(1/(sinAcosA))`
R.H.S. = tan A + cot A
= `sinA/cosA + cosA/sinA`
= `(sin^2A + cos^2A)/(sinAcosA)`
= `1/(sinAcosA)`
L.H.S. = R.H.S.
APPEARS IN
RELATED QUESTIONS
Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
`(sintheta - 2sin^3theta)/(2costheta - costheta) =tan theta`
Prove the following trigonometric identity.
`(sin theta - cos theta + 1)/(sin theta + cos theta - 1) = 1/(sec theta - tan theta)`
Prove that: `sqrt((sec theta - 1)/(sec theta + 1)) + sqrt((sec theta + 1)/(sec theta - 1)) = 2 cosec theta`
If x = a sec θ cos ϕ, y = b sec θ sin ϕ and z = c tan θ, show that `x^2/a^2 + y^2/b^2 - x^2/c^2 = 1`
If 5 `tan theta = 4,"write the value of" ((cos theta - sintheta))/(( cos theta + sin theta))`
Prove the following identity :
(secA - cosA)(secA + cosA) = `sin^2A + tan^2A`
If `asin^2θ + bcos^2θ = c and p sin^2θ + qcos^2θ = r` , prove that (b - c)(r - p) = (c - a)(q - r)
Prove that `( 1 + sin θ)/(1 - sin θ) = 1 + 2 tan θ/cos θ + 2 tan^2 θ` .
Prove that `(sin (90° - θ))/cos θ + (tan (90° - θ))/cot θ + (cosec (90° - θ))/sec θ = 3`.
Prove that `(tan θ + sin θ)/(tan θ - sin θ) = (sec θ + 1)/(sec θ - 1)`
