Advertisements
Advertisements
प्रश्न
Prove the following identities:
`(sinA - cosA + 1)/(sinA + cosA - 1) = cosA/(1 - sinA)`
Advertisements
उत्तर
`(sinA-cosA+1)/(sinA+cosA-1)`
= `(sinA - cosA + 1)/(sinA + cosA - 1) xx (sinA - (cosA - 1))/(sinA - (cosA - 1))`
= `(sinA - cosA + 1)^2/(sin^2A - (cosA - 1)^2)`
= `(sin^2A + cos^2A + 1 - 2sinAcosA - 2cosA + 2sinA)/(sin^2A - cos^2A - 1 + 2cosA)`
= `(1 + 1 - 2sinAcosA - 2cosA + 2sinA)/(-cos^2A - cos^2A + 2cosA)`
= `(2(1 - cosA) + 2sinA(1 - cosA))/(2cosA(1 - cosA)`
= `(1 + sinA)/cosA`
= `(1 + sinA)/cosA xx (1 - sinA)/(1 - sinA)`
= `cos^2A/(cosA(1 - sinA))`
= `cosA/(1 - sinA)`
संबंधित प्रश्न
Prove the following trigonometric identities.
`1/(sec A + tan A) - 1/cos A = 1/cos A - 1/(sec A - tan A)`
Prove the following trigonometric identities.
`(cot A + tan B)/(cot B + tan A) = cot A tan B`
Prove the following identities:
sec2A + cosec2A = sec2A . cosec2A
Prove the following identities:
`cot^2A((secA - 1)/(1 + sinA)) + sec^2A((sinA - 1)/(1 + secA)) = 0`
If `sin theta = 1/2 , " write the value of" ( 3 cot^2 theta + 3).`
Prove the following identity :
`(1 + cotA)^2 + (1 - cotA)^2 = 2cosec^2A`
If x = acosθ , y = bcotθ , prove that `a^2/x^2 - b^2/y^2 = 1.`
Without using trigonometric table , evaluate :
`cos90^circ + sin30^circ tan45^circ cos^2 45^circ`
If sec θ + tan θ = m, show that `(m^2 - 1)/(m^2 + 1) = sin theta`
Prove the following identities.
sec4 θ (1 – sin4 θ) – 2 tan2 θ = 1
