Advertisements
Advertisements
प्रश्न
Prove the following identity :
`sinA/(1 + cosA) + (1 + cosA)/sinA = 2cosecA`
Advertisements
उत्तर
`sinA/(1 + cosA) + (1 + cosA)/sinA = 2cosecA`
`(1 + cosA)/sinA + sinA/(1 + cosA)`
= `((1 + cosA)^2 + sin^2A)/(sinA(1 + cosA))`
= `(1 + 2cosA + cos^2A + sin^2A)/(sinA(1 + cosA))`
= `(2 + 2cosA)/(sinA(1 + cosA))`
= `(2(1 + cosA))/(sinA(1 + cosA)` [`sin^2A + cos^2A = 1`]
= 2 cosec A
APPEARS IN
संबंधित प्रश्न
Prove that sin6θ + cos6θ = 1 – 3 sin2θ. cos2θ.
Prove that (1 + cot θ – cosec θ)(1+ tan θ + sec θ) = 2
Show that : tan 10° tan 15° tan 75° tan 80° = 1
`sin theta (1+ tan theta) + cos theta (1+ cot theta) = ( sectheta+ cosec theta)`
`(1-tan^2 theta)/(cot^2-1) = tan^2 theta`
If `sin theta = 1/2 , " write the value of" ( 3 cot^2 theta + 3).`
Prove the following identity :
`sqrt(cosec^2q - 1) = "cosq cosecq"`
Prove that `sin(90^circ - A).cos(90^circ - A) = tanA/(1 + tan^2A)`
The value of tan A + sin A = M and tan A - sin A = N.
The value of `("M"^2 - "N"^2) /("MN")^0.5`
If sin A = `1/2`, then the value of sec A is ______.
