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प्रश्न
`(sin A)/(1 + cos A) + (1 + cos A)/(sin A)` = 2 cosec A
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उत्तर
LHS = `((sin^2 A + ( 1 + cos A)^2)/((1 + cos A)sin A))`
= `(sin^2 A + 1 + cos^2 A + 2 cos A)/((1 + cos A) sin A)`
= `(1 + 1 + 2 cos A)/((1 + cos A) sin A)`
= `(2(1 + cos A))/((1 + cos A)sin A)`
= 2 cosec A
= RHS
Hence proved.
संबंधित प्रश्न
If sinθ + sin2 θ = 1, prove that cos2 θ + cos4 θ = 1
Prove the following trigonometric identities
`(1 + tan^2 theta)/(1 + cot^2 theta) = ((1 - tan theta)/(1 - cot theta))^2 = tan^2 theta`
cosec4 θ − cosec2 θ = cot4 θ + cot2 θ
Write True' or False' and justify your answer the following :
The value of sin θ+cos θ is always greater than 1 .
Prove that:
tan (55° + x) = cot (35° – x)
Prove that: 2(sin6 θ + cos6 θ) – 3 (sin4 θ + cos4 θ) + 1 = 0.
If sec θ + tan θ = m, show that `(m^2 - 1)/(m^2 + 1) = sin theta`
If `sec θ + tan θ = sqrt(3)`, complete the activity to find the value of sec θ – tan θ.
Activity:
`square = 1 + tan^2θ` ...[Fundamental trigonometric identity]
`square - tan^2θ = 1`
`(sec θ + tan θ) . (sec θ - tan θ) = square`
`sqrt(3) . (sec θ - tan θ) = 1`
`(sec θ - tan θ) = square`
Prove that cosec θ – cot θ = `(sin θ)/(1 + cos θ)`.
Prove that `(cot A + "cosec" A - 1)/(cot A - "cosec" A + 1) = (1 + cos A)/(sin A)`.
