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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
рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНрди
Prove the following trigonometric identities:
`sin theta/(1 - cos theta) = cosec theta + cot theta`
Prove the following trigonometric identities.
`(cos^2 theta)/sin theta - cosec theta + sin theta = 0`
Prove the following trigonometric identities:
`((1 + sin theta)^2 + (1 - sin theta)^2)/(2cos^2 theta) = (1 + sin^2 theta)/(1 - sin^2 theta)`
Prove the following trigonometric identities.
`(1 + cot A + tan A)(sin A - cos A) = sec A/(cosec^2 A) - (cosec A)/sec^2 A = sin A tan A - cos A cot A`
Prove that: `sqrt((sec theta - 1)/(sec theta + 1)) + sqrt((sec theta + 1)/(sec theta - 1)) = 2 cosec theta`
Prove the following identities:
`1/(1 + cosA) + 1/(1 - cosA) = 2cosec^2A`
Prove the following identities:
`(1 - 2sin^2A)^2/(cos^4A - sin^4A) = 2cos^2A - 1`
If 2 sin A – 1 = 0, show that: sin 3A = 3 sin A – 4 sin3 A
Prove that:
(sin A + cos A) (sec A + cosec A) = 2 + sec A cosec A
`1 + (tan^2 θ)/((1 + sec θ)) = sec θ`
If `cos theta = 7/25 , "write the value of" ( tan theta + cot theta).`
Write the value of tan1° tan 2° ........ tan 89° .
If x = a sin θ and y = bcos θ , write the value of`(b^2 x^2 + a^2 y^2)`
Prove the following identity :
`(1 + cosA)/(1 - cosA) = (cosecA + cotA)^2`
Prove the following identity :
`(cosecA)/(cosecA - 1) + (cosecA)/(cosecA + 1) = 2sec^2A`
Prove the following identity :
`(secA - 1)/(secA + 1) = sin^2A/(1 + cosA)^2`
Prove the following identities.
`costheta/(1 + sintheta)` = sec θ – tan θ
Prove the following identities.
sec4 θ (1 – sin4 θ) – 2 tan2 θ = 1
If sinA + sin2A = 1, then the value of the expression (cos2A + cos4A) is ______.
`sqrt((1 - cos^2theta) sec^2 theta) = tan theta`
