Advertisements
Advertisements
प्रश्न
Prove that `(1 + sin B)/(cos B) + (cos B)/(1 + sin B) = 2 sec B`.
Advertisements
उत्तर
L.H.S = `(1 + sin B)/(cos B) + (cos B)/(1 + sin B)`
= `((1 + sin B)^2 + cos^2B)/(cos B(1 + sin B))`
= `(1 + 2 sin B + sin^2B + cos^2B)/(cos B(1 + sin B))` ...[∵ (a + b)2 = a2 + 2ab + b2]
= `(1 + 2 sin B + 1)/(cos B(1 + sin B))` ...[∵ sin2B + cos2B = 1]
= `(2 + 2 sin B)/(cos B(1 + sin B))`
= `(2(1 + sin B))/(cos B(1 + sin B))`
= `2/(cos B)`
= 2 sec B
= R.H.S.
∴ `(1 + sin B)/(cos B) + (cos B)/(1 + sin B) = 2 sec B`
APPEARS IN
संबंधित प्रश्न
Evaluate
`(sin ^2 63^@ + sin^2 27^@)/(cos^2 17^@+cos^2 73^@)`
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(cosec θ – cot θ)^2 = (1-cos theta)/(1 + cos theta)`
Prove the following trigonometric identities.
`(tan A + tan B)/(cot A + cot B) = tan A tan B`
Prove that:
`(tanA + 1/cosA)^2 + (tanA - 1/cosA)^2 = 2((1 + sin^2A)/(1 - sin^2A))`
If `cosA/cosB = m` and `cosA/sinB = n`, show that : (m2 + n2) cos2 B = n2.
`1/((1+tan^2 theta)) + 1/((1+ tan^2 theta))`
`1+ (cot^2 theta)/((1+ cosec theta))= cosec theta`
`tan theta/(1+ tan^2 theta)^2 + cottheta/(1+ cot^2 theta)^2 = sin theta cos theta`
Prove the following identities:
`(cot^2 theta (sec theta - 1))/((1 + sin theta)) + (sec^2 theta(sin theta - 1))/((1 + sec theta)) = 0`
If a cos θ + b sin θ = m and a sin θ – b cos θ = n, prove that (m2 + n2) = (a2 + b2).
If cosec2 θ (1 + cos θ) (1 − cos θ) = λ, then find the value of λ.
sec4 A − sec2 A is equal to
If x = r sin θ cos ϕ, y = r sin θ sin ϕ and z = r cos θ, then
Prove the following identity :
`tanA - cotA = (1 - 2cos^2A)/(sinAcosA)`
Prove the following identity :
`(cosecA)/(cosecA - 1) + (cosecA)/(cosecA + 1) = 2sec^2A`
Prove the following identity :
`(1 + cosA)/(1 - cosA) = tan^2A/(secA - 1)^2`
If A = 60°, B = 30° verify that tan( A - B) = `(tan A - tan B)/(1 + tan A. tan B)`.
Prove the following identities.
`costheta/(1 + sintheta)` = sec θ – tan θ
Prove that `(cot A)/(1 - cot A) + (tan A)/(1 - tan A) = -1`.
Prove that `(1 + sec A)/(sec A) = (sin^2A)/(1 - cos A)`.
