Advertisements
Advertisements
प्रश्न
Prove the following trigonometric identity:
`sqrt((1 + sin A)/(1 - sin A)) = sec A + tan A`
Advertisements
उत्तर
`sqrt((1 + sin A)/(1 - sin A)) = sec A + tan A`
LHS = `sqrt((1 + sin A)/(1 - sin A)`
Rationalize the numerator abd denominator with `sqrt(1 + sin A)`
LHS = `sqrt(((1 + sin A)(1 + sin A))/((1 - sin A)(1 + sin A)))`
= `sqrt((1 + sin A)^2/(1 - sin^2 A))`
= `sqrt((1 + sin A)^2/(cos^2 A))`
= `(1 + sin A)/(cos A)`
= `1/(cos A) + (sin A)/(cos A)`
= sec A + tan A
= RHS
APPEARS IN
संबंधित प्रश्न
Prove that:
sec2θ + cosec2θ = sec2θ x cosec2θ
Prove the following identities:
`(i) (sinθ + cosecθ)^2 + (cosθ + secθ)^2 = 7 + tan^2 θ + cot^2 θ`
`(ii) (sinθ + secθ)^2 + (cosθ + cosecθ)^2 = (1 + secθ cosecθ)^2`
`(iii) sec^4 θ– sec^2 θ = tan^4 θ + tan^2 θ`
Prove the following trigonometric identities.
(1 + tan2θ) (1 − sinθ) (1 + sinθ) = 1
Prove the following trigonometric identities.
`(sec A - tan A)/(sec A + tan A) = (cos^2 A)/(1 + sin A)^2`
Prove the following trigonometric identities.
`cos A/(1 - tan A) + sin A/(1 - cot A) = sin A + cos A`
Prove the following trigonometric identities
sec4 A(1 − sin4 A) − 2 tan2 A = 1
Prove the following identities:
`cot^2A/(cosecA + 1)^2 = (1 - sinA)/(1 + sinA)`
Prove the following identities:
`sqrt((1 + sinA)/(1 - sinA)) = sec A + tan A`
Write the value of `cosec^2 theta (1+ cos theta ) (1- cos theta).`
Write the value of `(1+ tan^2 theta ) ( 1+ sin theta ) ( 1- sin theta)`
If x = a sec θ and y = b tan θ, then b2x2 − a2y2 =
Prove the following identity :
`(1 + tan^2θ)sinθcosθ = tanθ`
If cosθ = `5/13`, then find sinθ.
Prove that `sqrt(2 + tan^2 θ + cot^2 θ) = tan θ + cot θ`.
Prove that: `sqrt((1 - cos θ)/(1 + cos θ)) = cosec θ - cot θ`.
Prove that:
`(sin A + cos A)/(sin A - cos A) + (sin A - cos A)/(sin A + cos A) = 2/(2 sin^2 A - 1)`
If sec θ = `25/7`, find the value of tan θ.
Solution:
1 + tan2 θ = sec2 θ
∴ 1 + tan2 θ = `(25/7)^square`
∴ tan2 θ = `625/49 - square`
= `(625 - 49)/49`
= `square/49`
∴ tan θ = `square/7` ........(by taking square roots)
If sinA + sin2A = 1, then the value of the expression (cos2A + cos4A) is ______.
Complete the following activity to prove:
cotθ + tanθ = cosecθ × secθ
Activity: L.H.S. = cotθ + tanθ
= `cosθ/sinθ + square/cosθ`
= `(square + sin^2theta)/(sinθ xx cosθ)`
= `1/(sinθ xx cosθ)` ....... ∵ `square`
= `1/sinθ xx 1/cosθ`
= `square xx secθ`
∴ L.H.S. = R.H.S.
Which of the following is true for all values of θ (0° ≤ θ ≤ 90°)?
