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рдкреНрд░рд╢реНрди
`(cot^2 theta ( sec theta - 1))/((1+ sin theta))+ (sec^2 theta(sin theta-1))/((1+ sec theta))=0`
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рдЙрддреНрддрд░
LHS= `(cot^2 theta ( sec theta - 1))/((1+ sin theta))+ (sec^2 theta(sin theta-1))/((1+ sec theta))`
=`(cos^2 theta/sin^2 theta(1/costheta-1))/((+ sin theta)) + (1/cos^2 theta(sin theta -1))/((1+ 1/cos theta))`
=`((cos^2 theta)/(sin^2 theta )((1- cos theta)/(cos theta)))/((1+sin theta))+ (((sin theta -1 ))/(cos ^2theta ))/(((cos theta + 1 )/(cos theta)))`
=`(cos^2 theta (1- cos theta))/(sin^2 theta cos theta (1+ sin theta))+ ((sin theta -1) cos theta)/((cos theta +1 ) cos^2 theta)`
=`(cos theta (1-cos theta))/((1- cos^2 theta)(1+ sin theta)) + ((sin theta -1)cos theta)/((costheta + 1 ) (1- sin^2 theta))`
=`(cos theta (1-cos theta))/((1- cos theta )( 1+ cos theta )(1+ sin theta)) + (-(1 sin theta ) cos theta)/((cos theta +1)(1-sin theta )(1+ sin theta))`
=`cos theta/((1+ cos theta )(1+ sin theta)) - cos theta/((cos theta +1)(1+ sin theta))`
= ЁЭЬГ
= RHS
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рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНрди
Prove the following trigonometric identity.
`cos^2 A + 1/(1 + cot^2 A) = 1`
Prove the following trigonometric identities.
`sqrt((1 - cos theta)/(1 + cos theta)) = cosec theta - cot theta`
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`tan^2 theta - sin^2 theta tan^2 theta sin^2 theta`
Prove the following trigonometric identities
tan2 A + cot2 A = sec2 A cosec2 A − 2
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`(cosecA - sinA)(secA - cosA) = 1/(tanA + cotA)`
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(1 + tan A . tan B)2 + (tan A – tan B)2 = sec2 A sec2 B
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`(sinA - cosA)(1 + tanA + cotA) = secA/(cosec^2A) - (cosecA)/(sec^2A)`
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(cosec A – sin A) (sec A – cos A) sec2 A = tan A
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Choose the correct alternative:
cot θ . tan θ = ?
Prove that `(tan(90 - theta) + cot(90 - theta))/("cosec" theta)` = sec θ
