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प्रश्न
Prove that: `(1 + cot^2 θ/(1 + cosec θ)) = cosec θ`.
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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 identities:
sec2A + cosec2A = sec2A . cosec2A
Prove the following identities:
(cosec A – sin A) (sec A – cos A) (tan A + cot A) = 1
` (sin theta - cos theta) / ( sin theta + cos theta ) + ( sin theta + cos theta ) / ( sin theta - cos theta ) = 2/ ((2 sin^2 theta -1))`
Four alternative answers for the following question are given. Choose the correct alternative and write its alphabet:
sin θ × cosec θ = ______
Prove the following identity :
`cosA/(1 - tanA) + sin^2A/(sinA - cosA) = cosA + sinA`
Find x , if `cos(2x - 6) = cos^2 30^circ - cos^2 60^circ`
Prove that `cos θ/sin(90° - θ) + sin θ/cos (90° - θ) = 2`.
Prove that sin2 5° + sin2 10° .......... + sin2 85° + sin2 90° = `9 1/2`.
The value of tan A + sin A = M and tan A - sin A = N.
The value of `("M"^2 - "N"^2) /("MN")^0.5`
Complete the following activity to prove:
cotθ + tanθ = cosecθ × secθ
Activity: L.H.S. = cotθ + tanθ
= `cosθ/sinθ + square/cosθ`
= `(square + sin^2theta)/(sinθ xx cosθ)`
= `1/(sinθ xx cosθ)` ....... ∵ `square`
= `1/sinθ xx 1/cosθ`
= `square xx secθ`
∴ L.H.S. = R.H.S.
