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प्रश्न
`sec theta (1- sin theta )( sec theta + tan theta )=1`
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उत्तर
LHS = `sec theta ( 1- sin theta )(sec theta + tan theta)`
=` (sec theta - sec theta sin theta) ( sec theta + tan theta)`
=` (sec theta - 1/(cos theta) xx sin theta )(sec theta+tantheta)`
=` (sec theta - tan theta ) ( sec theta + tan theta)`
= `sec ^2 theta - tan ^2 theta`
= 1
= RHS
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संबंधित प्रश्न
Prove that `(sin theta)/(1-cottheta) + (cos theta)/(1 - tan theta) = cos theta + sin theta`
Prove the following trigonometric identities.
(1 + tan2θ) (1 − sinθ) (1 + sinθ) = 1
Prove the following trigonometric identities.
`(cos^2 theta)/sin theta - cosec theta + sin theta = 0`
Prove the following identities:
(sec A – cos A) (sec A + cos A) = sin2 A + tan2 A
Prove the following identities:
`cosecA + cotA = 1/(cosecA - cotA)`
If sin A + cos A = m and sec A + cosec A = n, show that : n (m2 – 1) = 2 m
If 2 sin A – 1 = 0, show that: sin 3A = 3 sin A – 4 sin3 A
` (sin theta - cos theta) / ( sin theta + cos theta ) + ( sin theta + cos theta ) / ( sin theta - cos theta ) = 2/ ((2 sin^2 theta -1))`
Write the value of `(sin^2 theta 1/(1+tan^2 theta))`.
Write the value of \[\cot^2 \theta - \frac{1}{\sin^2 \theta}\]
Prove the following identity :
cosecθ(1 + cosθ)(cosecθ - cotθ) = 1
Prove the following identity :
`cosec^4A - cosec^2A = cot^4A + cot^2A`
Prove the following identity :
(secA - cosA)(secA + cosA) = `sin^2A + tan^2A`
Prove the following identity :
`sec^2A.cosec^2A = tan^2A + cot^2A + 2`
Prove the following identity :
`(1 + cosA)/(1 - cosA) = (cosecA + cotA)^2`
Express (sin 67° + cos 75°) in terms of trigonometric ratios of the angle between 0° and 45°.
Prove that sin( 90° - θ ) sin θ cot θ = cos2θ.
Prove that `(cos^2theta)/(sintheta) + sintheta` = cosec θ
Prove that `"cot A"/(1 - cot"A") + "tan A"/(1 - tan "A")` = – 1
If cot θ = `40/9`, find the values of cosec θ and sinθ,
We have, 1 + cot2θ = cosec2θ
1 + `square` = cosec2θ
1 + `square` = cosec2θ
`(square + square)/square` = cosec2θ
`square/square` = cosec2θ ......[Taking root on the both side]
cosec θ = `41/9`
and sin θ = `1/("cosec" θ)`
sin θ = `1/square`
∴ sin θ = `9/41`
The value is cosec θ = `41/9`, and sin θ = `9/41`
