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प्रश्न
Prove that: `1/(cosec"A" - cot"A") - 1/sin"A" = 1/sin"A" - 1/(cosec"A" + cot"A")`
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उत्तर
`= 1/(cosectheta-cottheta)xx (cosectheta+cottheta)/(cosectheta+cottheta)-1/sintheta`
`= (cosectheta+cottheta)/(cosec^2theta-cot^2theta) - 1/sintheta`
`cosectheta+cottheta - 1/sintheta`
`1/sintheta+costheta/sintheta - 1/sintheta`
`1/sintheta+(costheta-1)/sinthetaxx(costheta+1)/(costheta+1)`
`1/sintheta+(cos^2theta-1)/((1+costheta)sintheta)`
`1/sintheta-(1-cos^2theta)/(sintheta(1+costheta))`
`1/sintheta - (sin2theta)/(sintheta(1+costheta))`
`1/sintheta-sintheta/(1+costheta)`
`1/sintheta - (sintheta/sintheta)/(1/sintheta+costheta/sintheta)`
`1/sintheta-1/(cosectheta+cottheta)`= RHS
संबंधित प्रश्न
Prove that ` \frac{\sin \theta -\cos \theta +1}{\sin\theta +\cos \theta -1}=\frac{1}{\sec \theta -\tan \theta }` using the identity sec2 θ = 1 + tan2 θ.
`cos^2 theta + 1/((1+ cot^2 theta )) =1`
If a cos `theta + b sin theta = m and a sin theta - b cos theta = n , "prove that "( m^2 + n^2 ) = ( a^2 + b^2 )`
Prove that:
`(sin^2θ)/(cosθ) + cosθ = secθ`
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`cosec^4A - cosec^2A = cot^4A + cot^2A`
Prove the following identity :
`cosecA + cotA = 1/(cosecA - cotA)`
Prove the following identities:
`(sec"A"-1)/(sec"A"+1)=(sin"A"/(1+cos"A"))^2`
Prove the following identity :
`tan^2A - tan^2B = (sin^2A - sin^2B)/(cos^2Acos^2B)`
Prove the following identities.
`sqrt((1 + sin theta)/(1 - sin theta)` = sec θ + tan θ
If sin θ + sin2 θ = 1 show that: cos2 θ + cos4 θ = 1
