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рдкреНрд░рд╢реНрди
`sqrt((1-cos theta)/(1+cos theta)) = (cosec theta - cot theta)`
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
If secθ + tanθ = p, show that `(p^{2}-1)/(p^{2}+1)=\sin \theta`
Prove that `\frac{\sin \theta -\cos \theta }{\sin \theta +\cos \theta }+\frac{\sin\theta +\cos \theta }{\sin \theta -\cos \theta }=\frac{2}{2\sin^{2}\theta -1}`
Prove that `(tan^2 theta)/(sec theta - 1)^2 = (1 + cos theta)/(1 - cos theta)`
Prove the following trigonometric identity.
`cos^2 A + 1/(1 + cot^2 A) = 1`
Prove the following trigonometric identities.
`1/(sec A - 1) + 1/(sec A + 1) = 2 cosec A cot A`
Prove the following trigonometric identities.
`(1 + tan^2 A) + (1 + 1/tan^2 A) = 1/(sin^2 A - sin^4 A)`
Prove the following identities:
`(cosecA)/(cosecA - 1) + (cosecA)/(cosecA + 1) = 2sec^2A`
If sin A + cos A = m and sec A + cosec A = n, show that : n (m2 – 1) = 2 m
Prove the following identities:
sec4 A (1 – sin4 A) – 2 tan2 A = 1
Write the value of `sin theta cos ( 90° - theta )+ cos theta sin ( 90° - theta )`.
Write the value of tan1° tan 2° ........ tan 89° .
If tan A =` 5/12` , find the value of (sin A+ cos A) sec A.
cos4 A − sin4 A is equal to ______.
Prove the following identity :
`sin^8θ - cos^8θ = (sin^2θ - cos^2θ)(1 - 2sin^2θcos^2θ)`
If sinA + cosA = m and secA + cosecA = n , prove that n(m2 - 1) = 2m
Prove that: (1+cot A - cosecA)(1 + tan A+ secA) =2.
Prove that sec θ. cosec (90° - θ) - tan θ. cot( 90° - θ ) = 1.
Prove that cosec2 (90° - θ) + cot2 (90° - θ) = 1 + 2 tan2 θ.
Prove that `((tan 20°)/(cosec 70°))^2 + ((cot 20°)/(sec 70°))^2 = 1`
If tan θ = `9/40`, complete the activity to find the value of sec θ.
Activity:
sec2θ = 1 + `square` ......[Fundamental trigonometric identity]
sec2θ = 1 + `square^2`
sec2θ = 1 + `square`
sec θ = `square`
