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प्रश्न
`(1+ tan theta + cot theta )(sintheta - cos theta) = ((sec theta)/ (cosec^2 theta)-( cosec theta)/(sec^2 theta))`
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उत्तर
LHS = `(1+ tan theta + cot theta )(sintheta - cos theta) `
=` sin theta + tan theta sin theta + cot theta sin theta - cos theta - tan theta cos theta - cot theta cos theta `
=`sin theta + tan theta sin theta + cos theta/sin theta xx sin theta - cos theta -sin theta/cos thetaxx cos theta - cot theta cos theta`
=`sin theta + tan theta sin theta + cos theta - cos theta - sin theta - cot theta cos theta`
=`tan theta sin theta - cot theta cos theta`
=`sin theta / cos theta xx 1/( cosec theta) - cos theta / sin theta xx 1/ sec theta`
=` 1/ (cosec theta) xx 1/ ( cosec theta ) xx sec theta - 1/ sec theta xx 1/ sec theta xx cosec theta`
=` sec theta / ( cosec^2 theta) - (cosec theta)/sec^2 theta`
= RHS
Hence, LHS = RHS
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संबंधित प्रश्न
Prove the following trigonometric identities.
`sqrt((1 - cos A)/(1 + cos A)) = cosec A - cot A`
Prove the following identities:
`cosA/(1 - sinA) = sec A + tan A`
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`1 - cos^2A/(1 + sinA) = sinA`
Prove the following identities:
`1/(sinA + cosA) + 1/(sinA - cosA) = (2sinA)/(1 - 2cos^2A)`
Prove that:
2 sin2 A + cos4 A = 1 + sin4 A
Prove that:
`1/(cosA + sinA - 1) + 1/(cosA + sinA + 1) = cosecA + secA`
If tan A = n tan B and sin A = m sin B, prove that `cos^2A = (m^2 - 1)/(n^2 - 1)`
`1/((1+ sin θ)) + 1/((1 - sin θ)) = 2 sec^2 θ`
`sqrt((1+cos theta)/(1-cos theta)) + sqrt((1-cos theta )/(1+ cos theta )) = 2 cosec theta`
Write the value of `(1 + tan^2 theta ) cos^2 theta`.
If 5 `tan theta = 4,"write the value of" ((cos theta - sintheta))/(( cos theta + sin theta))`
If `sqrt(3) sin theta = cos theta and theta ` is an acute angle, find the value of θ .
Prove that:
`(sin^2θ)/(cosθ) + cosθ = secθ`
If tanθ `= 3/4` then find the value of secθ.
Prove the following identity :
`(tanθ + sinθ)/(tanθ - sinθ) = (secθ + 1)/(secθ - 1)`
Prove that sin (90° - θ) cos (90° - θ) = tan θ. cos2θ.
Prove that `( tan A + sec A - 1)/(tan A - sec A + 1) = (1 + sin A)/cos A`.
If (sin α + cosec α)2 + (cos α + sec α)2 = k + tan2α + cot2α, then the value of k is equal to
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
If sin A = `1/2`, then the value of sec A is ______.
