Advertisements
Advertisements
प्रश्न
Prove the following trigonometric identities.
`(1 - sin theta)/(1 + sin theta) = (sec theta - tan theta)^2`
उत्तर
We have to prove `(1 - sin theta)/(1 + sin theta) = (sec theta - tan theta)^2`
We know that, `sin^2 theta + cos^2 theta = 1`
Multiplying both numerator and denominator by `(1 - sin theta)` we have
`(1 - sin theta)/(1 + sin theta) = ((1 - sin theta)(1 - sin theta))/((1 + sin theta)(1 - sin theta))`
`= (1 - sin theta)^2/(1 - sin^2 theta)`
`= ((1 - sin theta)/cos theta)^2`
`= (1/cos theta - sin theta/cos theta)^2`
`= (sec theta - tan theta)^2`
APPEARS IN
संबंधित प्रश्न
If (secA + tanA)(secB + tanB)(secC + tanC) = (secA – tanA)(secB – tanB)(secC – tanC) prove that each of the side is equal to ±1. We have,
Prove the following trigonometric identities. `(1 - cos A)/(1 + cos A) = (cot A - cosec A)^2`
Prove the following trigonometric identities.
`1/(sec A + tan A) - 1/cos A = 1/cos A - 1/(sec A - tan A)`
Prove the following identities:
`sqrt((1 - cosA)/(1 + cosA)) = cosec A - cot A`
Prove the following identities:
`(1 - 2sin^2A)^2/(cos^4A - sin^4A) = 2cos^2A - 1`
Prove that:
`cot^2A/(cosecA - 1) - 1 = cosecA`
`1/((1+tan^2 theta)) + 1/((1+ tan^2 theta))`
If `sin theta = 1/2 , " write the value of" ( 3 cot^2 theta + 3).`
If `cosec theta = 2x and cot theta = 2/x ," find the value of" 2 ( x^2 - 1/ (x^2))`
If `sec theta = x ,"write the value of tan" theta`.
Write True' or False' and justify your answer the following :
The value of sin θ+cos θ is always greater than 1 .
If a cot θ + b cosec θ = p and b cot θ − a cosec θ = q, then p2 − q2
9 sec2 A − 9 tan2 A is equal to
If sec θ + tan θ = m, show that `(m^2 - 1)/(m^2 + 1) = sin theta`
The value of sin2θ + `1/(1 + tan^2 theta)` is equal to
Choose the correct alternative:
Which is not correct formula?
Prove that `sintheta/(sectheta+ 1) +sintheta/(sectheta - 1)` = 2 cot θ
If tan θ + sec θ = l, then prove that sec θ = `(l^2 + 1)/(2l)`.
Prove the following identity:
(sin2θ – 1)(tan2θ + 1) + 1 = 0
