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प्रश्न
Prove that `(sin θ tan θ)/(1 - cos θ) = 1 + sec θ.`
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उत्तर
LHS = `( sin θ tan θ)/(1 - cos θ)`
= `(sin θ. (sin θ)/(cos θ))/(1 - cos θ)`
= `sin^2 θ/(cos θ( 1 - cos θ))`
= `((1 - cos θ)(1 + cos θ))/(cos θ(1 - cos θ))`
= `(1 + cos θ)/(cos θ) = 1/(cos θ) + cos θ/cos θ`
= sec θ + 1
= RHS
Hence proved.
संबंधित प्रश्न
Show that `sqrt((1+cosA)/(1-cosA)) = cosec A + cot A`
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`(sin theta - cos theta + 1)/(sin theta + cos theta - 1) = 1/(sec theta - tan theta)`
Prove that:
`1/(sinA - cosA) - 1/(sinA + cosA) = (2cosA)/(2sin^2A - 1)`
Prove the following identity :
( 1 + cotθ - cosecθ) ( 1 + tanθ + secθ)
Prove the following identities.
`sqrt((1 + sin theta)/(1 - sin theta)` = sec θ + tan θ
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