Advertisements
Advertisements
प्रश्न
Prove the following identity :
`(tanθ + secθ - 1)/(tanθ - secθ + 1) = (1 + sinθ)/(cosθ)`
Advertisements
उत्तर
LHS = `(tanθ + secθ - 1)/(tanθ - secθ + 1) `
= `(tanθ + secθ - {sec^2θ - tan^2θ})/(1 + tanθ -secθ)`
= `(tanθ + secθ - {(secθ + tanθ)(secθ - tanθ)})/(1 + tanθ - secθ)`
= `([tanθ + secθ]{1 - (secθ - tanθ)})/[[1 + tanθ - secθ]` = `([tanθ + secθ][1 + tanθ - secθ])/[[1 + tanθ - secθ]]`
= `[tanθ + secθ] = (1 + sinθ)/cosθ` = RHS
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`(cosec A)/(cosec A - 1) + (cosec A)/(cosec A = 1) = 2 sec^2 A`
Prove that:
`(sinA - cosA)(1 + tanA + cotA) = secA/(cosec^2A) - (cosecA)/(sec^2A)`
`sin theta (1+ tan theta) + cos theta (1+ cot theta) = ( sectheta+ cosec theta)`
`tan theta /((1 - cot theta )) + cot theta /((1 - tan theta)) = (1+ sec theta cosec theta)`
Prove the following identities:
`(cos theta "cosec" theta - sin theta sec theta )/(cos theta + sin theta) = "cosec" theta - sec theta`
Prove the following identity :
sinθcotθ + sinθcosecθ = 1 + cosθ
Prove the following identity :
`(sinA - sinB)/(cosA + cosB) + (cosA - cosB)/(sinA + sinB) = 0`
Prove that `(cos θ)/(1 - sin θ) = (1 + sin θ)/(cos θ)`.
Prove that cot θ. tan (90° - θ) - sec (90° - θ). cosec θ + 1 = 0.
Prove the following identities.
sec4 θ (1 – sin4 θ) – 2 tan2 θ = 1
