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प्रश्न
Prove that `(cos θ)/(1 - sin θ) = (1 + sin θ)/(cos θ)`.
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उत्तर
L.H.S. = `cos θ/(1 - sin θ)`
= `(cos θ(1 + sin θ))/((1 - sin θ)(1 + sin θ))`
= `(cos θ(1 + sin θ))/(1 - sin^2θ)`
= `(cos θ(1 + sin θ))/(cos^2 θ)`
= `( 1 + sin θ)/cos θ`
Hence proved.
संबंधित प्रश्न
`Prove the following trigonometric identities.
`(sec A - tan A)^2 = (1 - sin A)/(1 + sin A)`
Prove the following identities:
`(secA - tanA)/(secA + tanA) = 1 - 2secAtanA + 2tan^2A`
Prove that:
`(sinA - sinB)/(cosA + cosB) + (cosA - cosB)/(sinA + sinB) = 0`
Prove that:
`(cosecA - sinA)(secA - cosA) = 1/(tanA + cotA)`
Show that none of the following is an identity:
(i) `cos^2theta + cos theta =1`
Write the value of`(tan^2 theta - sec^2 theta)/(cot^2 theta - cosec^2 theta)`
\[\frac{1 + \tan^2 A}{1 + \cot^2 A}\]is equal to
Prove the following identity :
`(1 - sin^2θ)sec^2θ = 1`
If `(cos alpha)/(cos beta)` = m and `(cos alpha)/(sin beta)` = n, then prove that (m2 + n2) cos2 β = n2
tan θ cosec2 θ – tan θ is equal to
