Advertisements
Advertisements
Question
Prove the following identities:
`cosA/(1 + sinA) + tanA = secA`
Advertisements
Solution
`cosA/(1+sinA)+tanA`
= `cosA/(1 + sinA) + sinA/cosA`
= `(cos^2A + sinA +(1+ sinA))/((1 + sinA)cosA)`
= `(cos^2A + sinA +sin^2A)/((1 + sinA)cosA)`
= `(1 + sinA)/((1 + sinA)cosA)`
= `1/cosA`
= sec A
Hence, proved.
APPEARS IN
RELATED QUESTIONS
Prove the following trigonometric identities.
`cot theta - tan theta = (2 cos^2 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.
`(tan^3 theta)/(1 + tan^2 theta) + (cot^3 theta)/(1 + cot^2 theta) = sec theta cosec theta - 2 sin theta cos theta`
Prove the following identities:
`1/(tan A + cot A) = cos A sin A`
If `cos theta = 2/3 , " write the value of" (4+4 tan^2 theta).`
If `tan theta = 1/sqrt(5), "write the value of" (( cosec^2 theta - sec^2 theta))/(( cosec^2 theta - sec^2 theta))`.
Prove that `(cos θ)/(1 - sin θ) = (1 + sin θ)/(cos θ)`.
Prove that `(tan θ)/(cot(90° - θ)) + (sec (90° - θ) sin (90° - θ))/(cosθ. cosec θ) = 2`.
If sin θ + cos θ = a and sec θ + cosec θ = b , then the value of b(a2 – 1) is equal to
If cosec A – sin A = p and sec A – cos A = q, then prove that `(p^2q)^(2/3) + (pq^2)^(2/3) = 1`.
