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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
Prove the following trigonometric identities.
`tan theta + 1/tan theta = sec theta cosec theta`
Prove the following identities:
`sinA/(1 + cosA) = cosec A - cot A`
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Write the value of ` cosec^2 (90°- theta ) - tan^2 theta`
If `tan theta = 1/sqrt(5), "write the value of" (( cosec^2 theta - sec^2 theta))/(( cosec^2 theta - sec^2 theta))`.
Prove the following identity :
tanA+cotA=secAcosecA
Prove the following identity :
`cosecA + cotA = 1/(cosecA - cotA)`
Prove that:
`(cos^3 θ + sin^3 θ)/(cos θ + sin θ) + (cos^3 θ - sin^3 θ)/(cos θ - sin θ) = 2`
Choose the correct alternative:
sec 60° = ?
Prove that `costheta/(1 + sintheta) = (1 - sintheta)/(costheta)`
