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प्रश्न
Prove that `(cot "A" + "cosec A" - 1)/(cot "A" - "cosec A" + 1) = (1 + cos "A")/sin "A"`
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उत्तर
LHS = `(cot "A" + "cosec A" - 1)/(cot "A" - "cosec A" + 1)`
= `((cot "A" + "cosec A") - ("cosec"^2 "A" - cot^2 "A"))/(cot "A" - "cosec A" + 1)`
= `((cot "A" + "cosec A")("cosec A" + cot "A")("cosec A" - cot "A"))/(cot "A" - "cosec A" + 1)`
= `((cot "A" + "cosec A") [1 - "cosec A" - cot "A"])/(cot"A"-"cosec A"+1)`
= `((cot "A" + "cosec A") (1-"cosec A"+cot"A"))/(1-"cosec A"+cot"A")`
= cot A + cosec A
= `cos"A"/sin"A"+1/sin"A"=(cos"A"+1)/sin"A"`
= `(1+cos"A")/sin"A"`
= RHS
Hence proved.
संबंधित प्रश्न
Prove the following trigonometric identities.
`(cos theta)/(cosec theta + 1) + (cos theta)/(cosec theta - 1) = 2 tan theta`
Prove the following trigonometric identities.
sin2 A cos2 B − cos2 A sin2 B = sin2 A − sin2 B
If tan A = n tan B and sin A = m sin B, prove that `cos^2A = (m^2 - 1)/(n^2 - 1)`
`1 + (tan^2 θ)/((1 + sec θ)) = sec θ`
`(sec theta -1 )/( sec theta +1) = ( sin ^2 theta)/( (1+ cos theta )^2)`
If \[\sin \theta = \frac{4}{5}\] what is the value of cotθ + cosecθ?
Prove the following identity :
`sec^4A - sec^2A = sin^2A/cos^4A`
If x = asecθ + btanθ and y = atanθ + bsecθ , prove that `x^2 - y^2 = a^2 - b^2`
Prove the following identities: sec2 θ + cosec2 θ = sec2 θ cosec2 θ.
Prove that: `(sin θ - 2sin^3 θ)/(2 cos^3 θ - cos θ) = tan θ`.
