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рдкреНрд░рд╢реНрди
`sqrt((1-cos theta)/(1+cos theta)) = (cosec theta - cot theta)`
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рдЙрддреНрддрд░
LHS = `sqrt((1-cos theta)/(1+ cos theta))`
=`sqrt(((1-cos theta))/((1+cos theta)) xx ((1- cos theta))/((1 - cos theta))`
=`sqrt((1-cos theta)^2 / (1-cos^2 theta))`
=`sqrt((1-cos theta)^2)/(sin^2 theta)`
=`(1-cos theta)/sin theta`
=`1/sin theta - cos theta/ sin theta`
=(ЁЭСРЁЭСЬЁЭСаЁЭСТЁЭСР ЁЭЬГ − cot ЁЭЬГ)
= RHS
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рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНрди
Prove the following trigonometric identities:
`(\text{i})\text{ }\frac{\sin \theta }{1-\cos \theta }=\text{cosec}\theta+\cot \theta `
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(tan theta)/(1-cot theta) + (cot theta)/(1-tan theta) = 1+secthetacosectheta`
[Hint: Write the expression in terms of sinθ and cosθ]
Prove the following trigonometric identities.
`cos A/(1 - tan A) + sin A/(1 - cot A) = sin A + cos A`
Prove the following identities:
`sinA/(1 + cosA) = cosec A - cot A`
Prove the following identities:
`sqrt((1 + sinA)/(1 - sinA)) = sec A + tan A`
Prove that:
(sec A − tan A)2 (1 + sin A) = (1 − sin A)
`(1+tan^2theta)(1+cot^2 theta)=1/((sin^2 theta- sin^4theta))`
`sin theta/((cot theta + cosec theta)) - sin theta /( (cot theta - cosec theta)) =2`
Write the value of `cosec^2 theta (1+ cos theta ) (1- cos theta).`
Prove the following identity :
`(tanθ + secθ - 1)/(tanθ - secθ + 1) = (1 + sinθ)/(cosθ)`
Prove the following identity :
`(secA - 1)/(secA + 1) = (1 - cosA)/(1 + cosA)`
Prove the following identity :
`cosA/(1 - tanA) + sin^2A/(sinA - cosA) = cosA + sinA`
Prove that: (1+cot A - cosecA)(1 + tan A+ secA) =2.
Prove that `tan A/(1 + tan^2 A)^2 + cot A/(1 + cot^2 A)^2 = sin A.cos A`
Prove that: `(sin θ - 2sin^3 θ)/(2 cos^3 θ - cos θ) = tan θ`.
Prove the following identities.
(sin θ + sec θ)2 + (cos θ + cosec θ)2 = 1 + (sec θ + cosec θ)2
If cos θ = `24/25`, then sin θ = ?
If cos 9α = sinα and 9α < 90°, then the value of tan5α is ______.
sin(45° + θ) – cos(45° – θ) is equal to ______.
If sin A = `1/2`, then the value of sec A is ______.
