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प्रश्न
`cosec theta (1+costheta)(cosectheta - cot theta )=1`
उत्तर
LHS = `cosec theta (1+ cos theta )( cosec theta - cot theta)`
=` (cosec theta + cosec theta xx cos theta)(cosec theta - cot theta)`
=` (cosec theta + 1/(sin theta) xx cos theta ) ( cosec theta - cot theta )`
=` ( cosec theta + cot theta )( cosec theta - cot theta)`
=` cosec^2 theta - cot^2 theta (∵ cosec^2 theta - cot^2 theta=1)`
= 1
= RHS
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संबंधित प्रश्न
Prove the identity (sin θ + cos θ)(tan θ + cot θ) = sec θ + cosec θ.
Prove the following trigonometric identities.
`tan theta - cot theta = (2 sin^2 theta - 1)/(sin theta cos theta)`
Prove the following identities:
`(1 - sinA)/(1 + sinA) = (secA - tanA)^2`
`cos^2 theta /((1 tan theta))+ sin ^3 theta/((sin theta - cos theta))=(1+sin theta cos theta)`
`(1+ tan^2 theta)/(1+ tan^2 theta)= (cos^2 theta - sin^2 theta)`
`(1-tan^2 theta)/(cot^2-1) = tan^2 theta`
Show that none of the following is an identity:
`tan^2 theta + sin theta = cos^2 theta`
Write the value of `(sin^2 theta 1/(1+tan^2 theta))`.
Write the value of `cosec^2 theta (1+ cos theta ) (1- cos theta).`
If tanθ `= 3/4` then find the value of secθ.
Write the value of cosec2 (90° − θ) − tan2 θ.
If \[\sin \theta = \frac{1}{3}\] then find the value of 9tan2 θ + 9.
Prove the following identity :
`(secA - 1)/(secA + 1) = (1 - cosA)/(1 + cosA)`
Prove the following identity :
`(1 + tan^2θ)sinθcosθ = tanθ`
Prove the following identity :
`(1 + sinθ)/(cosecθ - cotθ) - (1 - sinθ)/(cosecθ + cotθ) = 2(1 + cotθ)`
For ΔABC , prove that :
`sin((A + B)/2) = cos"C/2`
Prove that `( tan A + sec A - 1)/(tan A - sec A + 1) = (1 + sin A)/cos A`.
Prove that sin2 5° + sin2 10° .......... + sin2 85° + sin2 90° = `9 1/2`.
If 5 sec θ – 12 cosec θ = 0, then find values of sin θ, sec θ
Prove that `(cot A - cos A)/(cot A + cos A) = (cos^2 A)/(1 + sin A)^2`
