Advertisements
Advertisements
प्रश्न
Prove that `(sin 70°)/(cos 20°) + (cosec 20°)/(sec 70°) - 2 cos 70° xx cosec 20°` = 0.
Advertisements
उत्तर
LHS = `(sin 70°)/(cos 20°) + (cosec 20°)/(sec 70°) - 2 cos 70° xx cosec 20°`
= `sin (90° - 20°)/(cos 20°) + (cosec(90° - 20°))/(sec 70°) - 2 cos 70° xx cosec 20°`
= `(cos 20°)/(cos 20°) + (sec 70°)/(sec 70°) - 2 cos 70° xx cosec 20°`
= 1 + 1 - 2cos (90° - 20°) . cosec 20°
= 2 - 2 sin 20°. `1/sin 20°`
= 2 - 2
= 0
= RHS
Hence proved.
संबंधित प्रश्न
Prove the following identities:
`cosecA + cotA = 1/(cosecA - cotA)`
Prove the following identities:
`(1 - cosA)/sinA + sinA/(1 - cosA)= 2cosecA`
`cos^2 theta /((1 tan theta))+ sin ^3 theta/((sin theta - cos theta))=(1+sin theta cos theta)`
`(cos^3 θ + sin^3 θ)/(cos θ + sin θ) + (cos ^3 θ - sin^3 θ)/(cos θ - sin θ) = 2`
If (cosec θ – sin θ) = a3 and (sec θ – cos θ) = b3, prove that a2b2(a2 + b2) = 1.
Eliminate θ, if
x = 3 cosec θ + 4 cot θ
y = 4 cosec θ – 3 cot θ
Write the value of cosec2 (90° − θ) − tan2 θ.
Prove the following identities.
`sqrt((1 + sin theta)/(1 - sin theta)` = sec θ + tan θ
`(1 + cot^2A)/(1 + tan^2A)` = ?
If `sec θ = 41/40`, then find values of sin θ, cot θ, cosec θ.
