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рдкреНрд░рд╢реНрди
`cot theta/((cosec theta + 1) )+ ((cosec theta +1 ))/ cot theta = 2 sec theta `
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рдЙрддреНрддрд░
LHS = `cot theta/((cosec theta + 1) )+ ((cosec theta +1 ))/ cot theta `
=`( cot ^2 theta + (cosec theta + 1 ) ^2 ) / ((cosec theta +1) cot theta)`
=` ( cot ^2 + cosec ^2 theta + 2 cosec theta +1 )/( (cosec theta +1) cot theta)`
=`( cot ^2 theta + cosec ^2 theta +2cosec theta + cosec ^2 theta - cot^2 theta)/((cosec theta +1 ) cot theta)`
=` (2 cosec^2 theta + 2 cosec theta)/(( cosec theta +1 ) cot theta)`
=`(2 cosec theta ( cosec theta +1))/(( cosec theta +1 ) cot theta)`
=` (2 cosec theta)/(cot theta)`
=`2 xx 1/sin theta xx sin theta/ cos theta`
= 2 sec ЁЭЬГ
= RHS
Hence, LHS = RHS
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рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНтАНрди
Prove the following identities:
`(i) 2 (sin^6 θ + cos^6 θ) –3(sin^4 θ + cos^4 θ) + 1 = 0`
`(ii) (sin^8 θ – cos^8 θ) = (sin^2 θ – cos^2 θ) (1 – 2sin^2 θ cos^2 θ)`
Prove the following trigonometric identities:
`(1 - cos^2 A) cosec^2 A = 1`
Prove the following trigonometric identities.
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Prove the following trigonometric identities
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`1/(1 - sinA) + 1/(1 + sinA) = 2sec^2A`
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`(1 + sinA)/cosA + cosA/(1 + sinA) = 2secA`
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`(1 - sinA)/(1 + sinA) = (secA - tanA)^2`
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`sin^8θ - cos^8θ = (sin^2θ - cos^2θ)(1 - 2sin^2θcos^2θ)`
For ΔABC , prove that :
`sin((A + B)/2) = cos"C/2`
Prove that `sqrt((1 + sin A)/(1 - sin A))` = sec A + tan A.
If tan A + sin A = m and tan A − sin A = n, then show that `m^2 - n^2 = 4 sqrt (mn)`.
If cosθ + sinθ = `sqrt2` cosθ, show that cosθ - sinθ = `sqrt2` sinθ.
Prove that: `1/(sec θ - tan θ) = sec θ + tan θ`.
If cot θ + tan θ = x and sec θ – cos θ = y, then prove that `(x^2y)^(2/3) – (xy^2)^(2/3)` = 1
Prove that `(sin^2theta)/(cos theta) + cos theta` = sec θ
To prove cot θ + tan θ = cosec θ × sec θ, complete the activity given below.
Activity:
L.H.S = `square`
= `square/sintheta + sintheta/costheta`
= `(cos^2theta + sin^2theta)/square`
= `1/(sintheta*costheta)` ......`[cos^2theta + sin^2theta = square]`
= `1/sintheta xx 1/square`
= `square`
= R.H.S
sec θ when expressed in term of cot θ, is equal to ______.
