Advertisements
Advertisements
प्रश्न
Prove that: `(1 + cot^2 θ/(1 + cosec θ)) = cosec θ`.
Advertisements
उत्तर
LHS = `(1 + cot^2 θ/(1 + cosec θ))`
= `(1 + cosec θ + cosec^2 θ - 1)/(1 + cosec θ)`
= `(cosec θ(1 + cosec θ))/(1 + cosec θ)`
= cosec θ
= RHS
Hence proved.
संबंधित प्रश्न
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)`
If m = a sec A + b tan A and n = a tan A + b sec A, then prove that : m2 – n2 = a2 – b2
Prove the following identities:
`sinA/(1 - cosA) - cotA = cosecA`
` (sin theta - cos theta) / ( sin theta + cos theta ) + ( sin theta + cos theta ) / ( sin theta - cos theta ) = 2/ ((2 sin^2 theta -1))`
Prove the following identities:
`(cos theta "cosec" theta - sin theta sec theta )/(cos theta + sin theta) = "cosec" theta - sec theta`
Prove the following identity :
`(cosecA - sinA)(secA - cosA)(tanA + cotA) = 1`
Prove the following identity :
`sec^4A - sec^2A = sin^2A/cos^4A`
Prove the following identity :
`(cot^2θ(secθ - 1))/((1 + sinθ)) = sec^2θ((1-sinθ)/(1 + secθ))`
Evaluate:
`(tan 65^circ)/(cot 25^circ)`
Prove that `(cos θ)/(1 - sin θ) = (1 + sin θ)/(cos θ)`.
