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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.
`1/(1 + sin A) + 1/(1 - sin A) = 2sec^2 A`
Prove the following trigonometric identities.
`((1 + sin theta - cos theta)/(1 + sin theta + cos theta))^2 = (1 - cos theta)/(1 + cos theta)`
Prove the following identities:
`(sec A - 1)/(sec A + 1) = (1 - cos A)/(1 + cos A)`
Prove the following identities:
`((1 + tan^2A)cotA)/(cosec^2A) = tan A`
Prove the following identities:
`cosA/(1 + sinA) + tanA = secA`
Prove the following identities:
`sqrt((1 + sinA)/(1 - sinA)) = cosA/(1 - sinA)`
Prove the following identities:
cosec4 A (1 – cos4 A) – 2 cot2 A = 1
If sin A + cos A = p and sec A + cosec A = q, then prove that : q(p2 – 1) = 2p.
If tan A = n tan B and sin A = m sin B, prove that `cos^2A = (m^2 - 1)/(n^2 - 1)`
Prove that:
`1/(sinA - cosA) - 1/(sinA + cosA) = (2cosA)/(2sin^2A - 1)`
Write the value of `(1 + tan^2 theta ) cos^2 theta`.
Write the value of `(cot^2 theta - 1/(sin^2 theta))`.
If sin θ + sin2 θ = 1, then cos2 θ + cos4 θ =
Prove the following identity :
`(cos^3A + sin^3A)/(cosA + sinA) + (cos^3A - sin^3A)/(cosA - sinA) = 2`
Prove the following identity :
`(cosecθ)/(tanθ + cotθ) = cosθ`
Prove that:
`(cot A - 1)/(2 - sec^2 A) = cot A/(1 + tan A)`
Prove that (sin θ + cosec θ)2 + (cos θ + sec θ)2 = 7 + tan2 θ + cot2 θ.
A moving boat is observed from the top of a 150 m high cliff moving away from the cliff. The angle of depression of the boat changes from 60° to 45° in 2 minutes. Find the speed of the boat in m/min.
Prove the following identities.
`sqrt((1 + sin theta)/(1 - sin theta)` = sec θ + tan θ
Which is not correct formula?
