Advertisements
Advertisements
प्रश्न
Prove the following identity :
`(tanθ + sinθ)/(tanθ - sinθ) = (secθ + 1)/(secθ - 1)`
Advertisements
उत्तर
LHS = `(tanθ + sinθ)/(tanθ - sinθ)`
= `(sinθ/cosθ + sinθ)/(sinθ/cosθ - sinθ) = (sinθ + sinθcosθ)/(sinθ + sinθcosθ)`
= `(sinθ(1 + cosθ))/sin(1 + cosθ) = (1 + cosθ)/(1 - cosθ)`
= `(1 + 1/secθ)/(1 - 1/secθ) = ((secθ + 1)/secθ)/((secθ - 1)/secθ)`
= `(secθ + 1)/(secθ - 1)`
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
tan2 θ − sin2 θ = tan2 θ sin2 θ
Prove the following identities:
`((1 + tan^2A)cotA)/(cosec^2A) = tan A`
`sin^6 theta + cos^6 theta =1 -3 sin^2 theta cos^2 theta`
If cosec2 θ (1 + cos θ) (1 − cos θ) = λ, then find the value of λ.
Prove the following identity :
`(cosA + sinA)^2 + (cosA - sinA)^2 = 2`
If sin θ = `1/2`, then find the value of θ.
Prove that: 2(sin6 θ + cos6 θ) – 3 (sin4 θ + cos4 θ) + 1 = 0.
Prove that `sqrt(2 + tan^2 θ + cot^2 θ) = tan θ + cot θ`.
If x sin3θ + y cos3 θ = sin θ cos θ and x sin θ = y cos θ , then show that x2 + y2 = 1.
sin2θ + sin2(90 – θ) = ?
