Advertisements
Advertisements
Question
Prove that `cosA/(1+sinA) + tan A = secA`
Advertisements
Solution
L.H.S `cosA/(1+sinA) + tan A`
`= (cos A(1-sinA))/((1+sinA)(1-sinA)) + sinA/cosA`
`= (cosA - sinAcosA)/(1-sin^2A) + sinA/cosA`
`= (cosA - sinAcosA)/cos^2A + sinA/cosA`
`= 1/cosA - sinA/cosA + sinA/cosA`
`= 1/cosA`
= secA
=R.H.S
APPEARS IN
RELATED QUESTIONS
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 trigonometric identities.
`cos theta/(1 + sin theta) = (1 - sin theta)/cos theta`
Prove the following trigonometric identities.
`(1 + sin θ)/cos θ+ cos θ/(1 + sin θ) = 2 sec θ`
Prove the following trigonometric identities
`(1 + tan^2 theta)/(1 + cot^2 theta) = ((1 - tan theta)/(1 - cot theta))^2 = tan^2 theta`
If `sin theta = x , " write the value of cot "theta .`
Prove the following identity :
tanA+cotA=secAcosecA
Prove that: `1/(sec θ - tan θ) = sec θ + tan θ`.
Given that sinθ + 2cosθ = 1, then prove that 2sinθ – cosθ = 2.
Prove the following that:
`tan^3θ/(1 + tan^2θ) + cot^3θ/(1 + cot^2θ)` = secθ cosecθ – 2 sinθ cosθ
If tan θ = `x/y`, then cos θ is equal to ______.
