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प्रश्न
`(sec theta -1 )/( sec theta +1) = ( sin ^2 theta)/( (1+ cos theta )^2)`
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उत्तर
LHS = `(sec theta-1)/(sec theta+1)`
=` (1/cos theta-1)/(1/ cos theta +1)`
=`((1-cos theta)/cos theta)/((1+ cos theta)/cos theta)`
=`(1-cos theta)/(1+costheta)`
=`((1-cos theta)(1+ cos theta))/((1+ cos theta)(1+ cos theta)) {"Dividing the numerator and
denominator by "(1+ cos theta)}`
=`(1- cos^2 theta)/((1+ cos theta )^2)`
=`(sin^2 theta)/((1+ cos theta) ^2)`
= RHS
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संबंधित प्रश्न
Prove that:
sec2θ + cosec2θ = sec2θ x cosec2θ
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`((1 + sin theta)^2 + (1 + sin theta)^2)/(2cos^2 theta) = (1 + sin^2 theta)/(1 - sin^2 theta)`
Prove the following trigonometric identities.
`(tan^2 A)/(1 + tan^2 A) + (cot^2 A)/(1 + cot^2 A) = 1`
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`cot theta/((cosec theta + 1) )+ ((cosec theta +1 ))/ cot theta = 2 sec theta `
If `( tan theta + sin theta ) = m and ( tan theta - sin theta ) = n " prove that "(m^2-n^2)^2 = 16 mn .`
If \[\sin \theta = \frac{1}{3}\] then find the value of 2cot2 θ + 2.
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`sin^8θ - cos^8θ = (sin^2θ - cos^2θ)(1 - 2sin^2θcos^2θ)`
Prove that:
`(cot A - 1)/(2 - sec^2 A) = cot A/(1 + tan A)`
Prove that sin( 90° - θ ) sin θ cot θ = cos2θ.
Prove the following identities: cot θ - tan θ = `(2 cos^2 θ - 1)/(sin θ cos θ)`.
Prove that: `1/(cosec"A" - cot"A") - 1/sin"A" = 1/sin"A" - 1/(cosec"A" + cot"A")`
Prove that
sec2A – cosec2A = `(2sin^2"A" - 1)/(sin^2"A"*cos^2"A")`
If sinθ – cosθ = 0, then the value of (sin4θ + cos4θ) is ______.
Let x1, x2, x3 be the solutions of `tan^-1((2x + 1)/(x + 1)) + tan^-1((2x - 1)/(x - 1))` = 2tan–1(x + 1) where x1 < x2 < x3 then 2x1 + x2 + x32 is equal to ______.
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Prove the following trigonometry identity:
(sin θ + cos θ)(cosec θ – sec θ) = cosec θ ⋅ sec θ – 2 tan θ
