Advertisements
Advertisements
प्रश्न
Prove the following identities:
`cot^2A((secA - 1)/(1 + sinA)) + sec^2A((sinA - 1)/(1 + secA)) = 0`
Advertisements
उत्तर
`cot^2A((secA - 1)/(1 + sinA)) + sec^2A((sinA - 1)/(1 + secA))`
= `cot^2A((secA - 1)/(1 + sinA) xx (secA + 1)/(secA + 1)) + sec^2A((sinA - 1)/(1 + secA))`
= `cot^2A[(sec^2A - 1)/((1 + sinA)(secA + 1))] + sec^2A((sinA - 1)/(1 + secA))`
= `cot^2A[(tan^2A)/((1 + sinA)(secA + 1))] + sec^2A((sinA - 1)/(1 + secA))`
= `1/((1 + sinA)(secA + 1)) + sec^2A((sinA - 1)/(1 + secA))`
= `(1 + sec^2A(sinA - 1)(1 + sinA))/((1 + sinA)(secA + 1))`
= `(1 + sec^2A(sin^2A - 1))/((1 + sinA)(secA + 1))`
= `(1 + sec^2A(-cos^2A))/((1 + sinA)(secA + 1))`
= `(1 - 1)/((1 + sinA)(secA + 1))`
= 0
APPEARS IN
संबंधित प्रश्न
If acosθ – bsinθ = c, prove that asinθ + bcosθ = `\pm \sqrt{a^{2}+b^{2}-c^{2}`
Prove the following trigonometric identities.
`(1 + cos θ + sin θ)/(1 + cos θ - sin θ) = (1 + sin θ)/cos θ`
Prove the following trigonometric identities.
(cosec θ − sec θ) (cot θ − tan θ) = (cosec θ + sec θ) ( sec θ cosec θ − 2)
Prove that:
`(tanA + 1/cosA)^2 + (tanA - 1/cosA)^2 = 2((1 + sin^2A)/(1 - sin^2A))`
`tan theta/(1+ tan^2 theta)^2 + cottheta/(1+ cot^2 theta)^2 = sin theta cos theta`
Simplify : 2 sin30 + 3 tan45.
Prove the following identity :
`(1 + cosA)/(1 - cosA) = (cosecA + cotA)^2`
Prove that `(tan θ + sin θ)/(tan θ - sin θ) = (sec θ + 1)/(sec θ - 1)`
Prove that:
`(cos^3 θ + sin^3 θ)/(cos θ + sin θ) + (cos^3 θ - sin^3 θ)/(cos θ - sin θ) = 2`
If `sqrt(3)` sin θ – cos θ = θ, then show that tan 3θ = `(3tan theta - tan^3 theta)/(1 - 3 tan^2 theta)`
