Advertisements
Advertisements
प्रश्न
(sec θ + tan θ) . (sec θ – tan θ) = ?
Advertisements
उत्तर
(sec θ + tan θ)(sec θ – tan θ)
= sec2θ – tan2θ ...[∵ (a + b)(a – b) = a2 – b2]
= 1 ...`[(∵ 1 + tan^2θ = sec^2θ),(∴ sec^2θ - tan^2θ = 1)]`
APPEARS IN
संबंधित प्रश्न
Evaluate sin25° cos65° + cos25° sin65°
Prove the following trigonometric identities.
`sin^2 A + 1/(1 + tan^2 A) = 1`
Prove the following trigonometric identities.
`(1 + sin θ)/cos θ+ cos θ/(1 + sin θ) = 2 sec θ`
Prove the following trigonometric identities. `(1 - cos A)/(1 + cos A) = (cot A - cosec A)^2`
Prove the following trigonometric identities.
`(1/(sec^2 theta - cos theta) + 1/(cosec^2 theta - sin^2 theta)) sin^2 theta cos^2 theta = (1 - sin^2 theta cos^2 theta)/(2 + sin^2 theta + cos^2 theta)`
Prove the following trigonometric identities
sec4 A(1 − sin4 A) − 2 tan2 A = 1
Prove the following identities:
(cosec A – sin A) (sec A – cos A) (tan A + cot A) = 1
Prove the following identities:
sec2 A . cosec2 A = tan2 A + cot2 A + 2
If a cos θ + b sin θ = m and a sin θ − b cos θ = n, then a2 + b2 =
Prove the following identity :
`(tanθ + secθ - 1)/(tanθ - secθ + 1) = (1 + sinθ)/(cosθ)`
Prove the following identity :
`cosec^4A - cosec^2A = cot^4A + cot^2A`
If m = a secA + b tanA and n = a tanA + b secA , prove that m2 - n2 = a2 - b2
Prove that (sin θ + cosec θ)2 + (cos θ + sec θ)2 = 7 + tan2 θ + cot2 θ.
Prove that sin2 θ + cos4 θ = cos2 θ + sin4 θ.
Prove that `(sin θ tan θ)/(1 - cos θ) = 1 + sec θ.`
If A = 60°, B = 30° verify that tan( A - B) = `(tan A - tan B)/(1 + tan A. tan B)`.
Without using a trigonometric table, prove that
`(cos 70°)/(sin 20°) + (cos 59°)/(sin 31°) - 8sin^2 30° = 0`.
Prove the following identities: cot θ - tan θ = `(2 cos^2 θ - 1)/(sin θ cos θ)`.
`(1 + cot^2A)/(1 + tan^2A)` = ?
Prove that `(1 + sin θ)/(1 - sin θ) = (sec θ + tan θ)^2`.
