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Question
If `cosec theta = 2x and cot theta = 2/x ," find the value of" 2 ( x^2 - 1/ (x^2))`
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Solution
2 `(x^2 - 1/(x^2))`
=`4/2(x^2 - 1/(x^2))`
=`1/2(4x^2 - 4/(x^2))`
=`1/2 [(2x)^2- (2/x)^2]`
=`1/2 [( cosec theta )^2 - (cot theta)^2]`
=`1/2 (cosec ^2 theta - cot^2 theta)`
=`1/2 (1)`
=`1/2`
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RELATED QUESTIONS
Prove the following trigonometric identities.
`1 + cot^2 theta/(1 + cosec theta) = cosec theta`
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`(cosecA - 1)/(cosecA + 1) = (cosA/(1 + sinA))^2`
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`cos^2A = (m^2 - 1)/(n^2 - 1)`
`sec theta (1- sin theta )( sec theta + tan theta )=1`
`(cot ^theta)/((cosec theta+1)) + ((cosec theta + 1))/cot theta = 2 sec theta`
`(sin theta)/((sec theta + tan theta -1)) + cos theta/((cosec theta + cot theta -1))=1`
If sin2 θ cos2 θ (1 + tan2 θ) (1 + cot2 θ) = λ, then find the value of λ.
Prove the following identity :
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Prove the following identity :
`sqrt((1 + sinq)/(1 - sinq)) + sqrt((1- sinq)/(1 + sinq))` = 2secq
Prove the following identity :
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Evaluate:
`(tan 65^circ)/(cot 25^circ)`
Prove that: 2(sin6 θ + cos6 θ) – 3 (sin4 θ + cos4 θ) + 1 = 0.
Prove that : `1 - (cos^2 θ)/(1 + sin θ) = sin θ`.
Prove that cot θ. tan (90° - θ) - sec (90° - θ). cosec θ + 1 = 0.
Prove that `[(1 + sin theta - cos theta)/(1 + sin theta + cos theta)]^2 = (1 - cos theta)/(1 + cos theta)`
If tan θ = `7/24`, then to find value of cos θ complete the activity given below.
Activity:
sec2θ = 1 + `square` ......[Fundamental tri. identity]
sec2θ = 1 + `square^2`
sec2θ = 1 + `square/576`
sec2θ = `square/576`
sec θ = `square`
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Prove that `sec"A"/(tan "A" + cot "A")` = sin A
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cotθ + tanθ = cosecθ × secθ
Activity: L.H.S. = cotθ + tanθ
= `cosθ/sinθ + square/cosθ`
= `(square + sin^2theta)/(sinθ xx cosθ)`
= `1/(sinθ xx cosθ)` ....... ∵ `square`
= `1/sinθ xx 1/cosθ`
= `square xx secθ`
∴ L.H.S. = R.H.S.
