Advertisements
Advertisements
प्रश्न
Prove the following identities:
`cot^2A((secA - 1)/(1 + sinA)) + sec^2A((sinA - 1)/(1 + secA)) = 0`
Advertisements
उत्तर
`cot^2A((secA - 1)/(1 + sinA)) + sec^2A((sinA - 1)/(1 + secA))`
= `cot^2A((secA - 1)/(1 + sinA) xx (secA + 1)/(secA + 1)) + sec^2A((sinA - 1)/(1 + secA))`
= `cot^2A[(sec^2A - 1)/((1 + sinA)(secA + 1))] + sec^2A((sinA - 1)/(1 + secA))`
= `cot^2A[(tan^2A)/((1 + sinA)(secA + 1))] + sec^2A((sinA - 1)/(1 + secA))`
= `1/((1 + sinA)(secA + 1)) + sec^2A((sinA - 1)/(1 + secA))`
= `(1 + sec^2A(sinA - 1)(1 + sinA))/((1 + sinA)(secA + 1))`
= `(1 + sec^2A(sin^2A - 1))/((1 + sinA)(secA + 1))`
= `(1 + sec^2A(-cos^2A))/((1 + sinA)(secA + 1))`
= `(1 - 1)/((1 + sinA)(secA + 1))`
= 0
APPEARS IN
संबंधित प्रश्न
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`cos A/(1 + sin A) + (1 + sin A)/cos A = 2 sec A`
Prove the following identities:
`(sec A - 1)/(sec A + 1) = (1 - cos A)/(1 + cos A)`
Prove the following identities:
`sqrt((1 + sinA)/(1 - sinA)) = cosA/(1 - sinA)`
Prove that `( sintheta - 2 sin ^3 theta ) = ( 2 cos ^3 theta - cos theta) tan theta`
If `tan theta = 1/sqrt(5), "write the value of" (( cosec^2 theta - sec^2 theta))/(( cosec^2 theta - sec^2 theta))`.
Prove the following identity :
`(1 + sinθ)/(cosecθ - cotθ) - (1 - sinθ)/(cosecθ + cotθ) = 2(1 + cotθ)`
Prove the following identity :
`(sec^2θ - sin^2θ)/tan^2θ = cosec^2θ - cos^2θ`
Prove that `cos θ/sin(90° - θ) + sin θ/cos (90° - θ) = 2`.
Prove the following:
`sintheta/(1 + cos theta) + (1 + cos theta)/sintheta` = 2cosecθ
(1 + sin A)(1 – sin A) is equal to ______.
