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प्रश्न
Prove the following identities:
`sqrt((1 - cosA)/(1 + cosA)) = sinA/(1 + cosA)`
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उत्तर
L.H.S. = `sqrt((1 - cosA)/(1 + cosA))`
= `sqrt((1 - cosA)/(1 + cosA) xx (1 + cosA)/(1 + cosA))`
= `sqrt((1 - cos^2A)/(1 + cosA)^2)`
= `sqrt(sin^2A/(1 + cosA)^2)`
= `sinA/(1 + cosA)` = R.H.S.
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संबंधित प्रश्न
Prove the following trigonometric identities
`cos theta/(1 - sin theta) = (1 + sin theta)/cos theta`
Prove the following trigonometric identities.
(1 + cot A − cosec A) (1 + tan A + sec A) = 2
If cos θ + cos2 θ = 1, prove that sin12 θ + 3 sin10 θ + 3 sin8 θ + sin6 θ + 2 sin4 θ + 2 sin2 θ − 2 = 1
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Prove that:
`tanA/(1 - cotA) + cotA/(1 - tanA) = secA "cosec" A + 1`
Prove that `sin(90^circ - A).cos(90^circ - A) = tanA/(1 + tan^2A)`
Proved that cosec2(90° - θ) - tan2 θ = cos2(90° - θ) + cos2 θ.
tan2θ – sin2θ = tan2θ × sin2θ. For proof of this complete the activity given below.
Activity:
L.H.S. = `square`
= `square (1 - (sin^2θ)/(tan^2θ))`
= `tan^2θ (1 - square/((sin^2θ)/(cos^2θ)))`
= `tan^2θ (1 - (sin^2θ)/1 xx (cos^2θ)/square)`
= `tan^2θ (1 - square)`
= `tan^2θ xx square` ...[1 – cos2θ = sin2θ]
= R.H.S.
If tan α + cot α = 2, then tan20α + cot20α = ______.
Prove the following identity:
(sin2θ – 1)(tan2θ + 1) + 1 = 0
