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प्रश्न
`(cos theta cosec theta - sin theta sec theta )/(costheta + sin theta) = cosec theta - sec theta`
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उत्तर
LHS = `(cos theta cosec theta - sin theta sec theta )/(costheta + sin theta)`
=`((cos theta sin theta)/(sin theta cos theta))/(cos theta + sin theta)`
=`(cos^2 theta - sin^2 theta)/(cos theta sin theta ( cos theta + sin theta))`
=`((cos theta + sin theta )( cos theta - sin theta))/(cos theta sin theta ( cos theta + sin theta))`
=`((cos theta - sin theta ))/(cos theta sin theta)`
=`1/ sin theta - 1/ cos theta`
=`cosec theta - sec theta`
= RHS
Hence, LHS = RHS
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संबंधित प्रश्न
Express the ratios cos A, tan A and sec A in terms of sin A.
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(tan theta)/(1-cot theta) + (cot theta)/(1-tan theta) = 1+secthetacosectheta`
[Hint: Write the expression in terms of sinθ and cosθ]
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(sin theta-2sin^3theta)/(2cos^3theta -costheta) = tan theta`
As observed from the top of an 80 m tall lighthouse, the angles of depression of two ships on the same side of the lighthouse of the horizontal line with its base are 30° and 40° respectively. Find the distance between the two ships. Give your answer correct to the nearest meter.
Prove the following identities:
`cosA/(1 + sinA) + tanA = secA`
Prove that:
`cosA/(1 + sinA) = secA - tanA`
Write the value of `3 cot^2 theta - 3 cosec^2 theta.`
If `cos theta = 7/25 , "write the value of" ( tan theta + cot theta).`
Prove the following identity :
`sinA/(1 + cosA) + (1 + cosA)/sinA = 2cosecA`
Prove the following identity :
`((1 + tan^2A)cotA)/(cosec^2A) = tanA`
Prove the following identity :
`(tanθ + sinθ)/(tanθ - sinθ) = (secθ + 1)/(secθ - 1)`
Prove that `[(1 + sin theta - cos theta)/(1 + sin theta + cos theta)]^2 = (1 - cos theta)/(1 + cos theta)`
Which is not correct formula?
Prove that cot2θ – tan2θ = cosec2θ – sec2θ.
Prove the following:
(sin α + cos α)(tan α + cot α) = sec α + cosec α
Simplify (1 + tan2θ)(1 – sinθ)(1 + sinθ)
Show that tan4θ + tan2θ = sec4θ – sec2θ.
Prove that `(1 + sec theta - tan theta)/(1 + sec theta + tan theta) = (1 - sin theta)/cos theta`
Complete the following activity to prove:
cotθ + tanθ = cosecθ × secθ
Activity: L.H.S. = cotθ + tanθ
= `cosθ/sinθ + square/cosθ`
= `(square + sin^2theta)/(sinθ xx cosθ)`
= `1/(sinθ xx cosθ)` ....... ∵ `square`
= `1/sinθ xx 1/cosθ`
= `square xx secθ`
∴ L.H.S. = R.H.S.
