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
Prove that (cosec A – sin A)(sec A – cos A) sec2 A = tan A.
Prove the following trigonometric identities.
`(sec A - tan A)/(sec A + tan A) = (cos^2 A)/(1 + sin A)^2`
if `cosec theta - sin theta = a^3`, `sec theta - cos theta = b^3` prove that `a^2 b^2 (a^2 + b^2) = 1`
Prove the following identities:
(1 – tan A)2 + (1 + tan A)2 = 2 sec2A
Prove the following identities:
cosec A(1 + cos A) (cosec A – cot A) = 1
Prove the following identities:
`(1 + sinA)/cosA + cosA/(1 + sinA) = 2secA`
Show that : tan 10° tan 15° tan 75° tan 80° = 1
cosec4 θ − cosec2 θ = cot4 θ + cot2 θ
Find the value of ` ( sin 50°)/(cos 40°)+ (cosec 40°)/(sec 50°) - 4 cos 50° cosec 40 °`
If a cos θ − b sin θ = c, then a sin θ + b cos θ =
Prove the following identity :
`sin^8θ - cos^8θ = (sin^2θ - cos^2θ)(1 - 2sin^2θcos^2θ)`
Prove that `sqrt((1 + sin A)/(1 - sin A))` = sec A + tan A.
Prove that (sin θ + cosec θ)2 + (cos θ + sec θ)2 = 7 + tan2 θ + cot2 θ.
Prove that sin4θ - cos4θ = sin2θ - cos2θ
= 2sin2θ - 1
= 1 - 2 cos2θ
Prove that: `(sec θ - tan θ)/(sec θ + tan θ ) = 1 - 2 sec θ.tan θ + 2 tan^2θ`
Prove that: 2(sin6θ + cos6θ) - 3 ( sin4θ + cos4θ) + 1 = 0.
If A = 30°, verify that `sin 2A = (2 tan A)/(1 + tan^2 A)`.
Proved that cosec2(90° - θ) - tan2 θ = cos2(90° - θ) + cos2 θ.
`(1 - tan^2 45^circ)/(1 + tan^2 45^circ)` = ?
If `sin θ + cos θ = sqrt(3)`, then show that tan θ + cot θ = 1.
