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प्रश्न
Prove that:
(cosec θ - sinθ )(secθ - cosθ ) ( tanθ +cot θ) =1
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उत्तर
Taking LHS
(cosec θ - sinθ )(secθ - cos θ ) ( tanθ +cot θ)
`(1/(sin theta )- sin theta )(1/(cos θ )- cosθ )((sin θ)/(cos θ) +(cos θ)/(sin θ))`
`=((1-sin^2 θ)/(sin θ)) ((1- cos ^2θ)/(cos θ)) ((sin^2 θ + cos^2 θ)/(sin θ . cos θ))`
`= (cos^2 θ)/( sin θ) xx (sin^2 θ)/(cos θ ) xx 1/(sinθ . cos θ )` = 1 = RHS
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संबंधित प्रश्न
Prove the following trigonometric identities.
`(1 + cos A)/sin A = sin A/(1 - cos A)`
Prove the following trigonometric identities.
`(1 + cos θ + sin θ)/(1 + cos θ - sin θ) = (1 + sin θ)/cos θ`
Prove the following identities:
`(cosecA)/(cosecA - 1) + (cosecA)/(cosecA + 1) = 2sec^2A`
Show that none of the following is an identity:
(i) `cos^2theta + cos theta =1`
Show that none of the following is an identity:
`sin^2 theta + sin theta =2`
Write the value of `( 1- sin ^2 theta ) sec^2 theta.`
If `sec theta + tan theta = x," find the value of " sec theta`
Prove the following identity :
`1/(cosA + sinA - 1) + 2/(cosA + sinA + 1) = cosecA + secA`
Prove that `(cos θ)/(1 - sin θ) = (1 + sin θ)/(cos θ)`.
Prove that: `(sec θ - tan θ)/(sec θ + tan θ ) = 1 - 2 sec θ.tan θ + 2 tan^2θ`
