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प्रश्न
Prove the following identities:
`cosA/(1 + sinA) + tanA = secA`
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उत्तर
`cosA/(1+sinA)+tanA`
= `cosA/(1 + sinA) + sinA/cosA`
= `(cos^2A + sinA +(1+ sinA))/((1 + sinA)cosA)`
= `(cos^2A + sinA +sin^2A)/((1 + sinA)cosA)`
= `(1 + sinA)/((1 + sinA)cosA)`
= `1/cosA`
= sec A
Hence, proved.
संबंधित प्रश्न
Prove the following trigonometric identities:
(i) (1 – sin2θ) sec2θ = 1
(ii) cos2θ (1 + tan2θ) = 1
Prove the following identities:
`(i) (sinθ + cosecθ)^2 + (cosθ + secθ)^2 = 7 + tan^2 θ + cot^2 θ`
`(ii) (sinθ + secθ)^2 + (cosθ + cosecθ)^2 = (1 + secθ cosecθ)^2`
`(iii) sec^4 θ– sec^2 θ = tan^4 θ + tan^2 θ`
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(1+ secA)/sec A = (sin^2A)/(1-cosA)`
[Hint : Simplify LHS and RHS separately.]
Prove the following trigonometric identities.
`sqrt((1 - cos theta)/(1 + cos theta)) = cosec theta - cot theta`
Prove the following trigonometric identities.
`(1 - cos theta)/sin theta = sin theta/(1 + cos theta)`
Prove the following identities:
`(sinAtanA)/(1 - cosA) = 1 + secA`
Prove the following identities:
`sqrt((1 - sinA)/(1 + sinA)) = cosA/(1 + sinA)`
Prove the following identities:
`cosecA - cotA = sinA/(1 + cosA)`
`(1 + cot^2 theta ) sin^2 theta =1`
Write True' or False' and justify your answer the following :
The value of sin θ+cos θ is always greater than 1 .
