Advertisements
Advertisements
Question
Prove the following identities:
`1/(cosA + sinA) + 1/(cosA - sinA) = (2cosA)/(2cos^2A - 1)`
Advertisements
Solution 1
`1/(cosA + sinA) + 1/(cosA - sinA)`
= `(cosA + sinA + cosA - sinA)/((cosA + sinA)(cosA - sinA)`
= `(2cosA)/(cos^2A - sin^2A)`
= `(2cosA)/(cos^2A - (1 - cos^2A))`
= `(2cosA)/(cos^2A - 1 + cos^2A)`
= `(2cosA)/(2cos^2A - 1)`
Solution 2
`1/(cosA + sinA) + 1/(cosA - sinA)`
`1/(cosA + sinA) + 1/(cosA - sinA) = ((cos A - sin A) + (cos A + sin A))/((cos A + ain A)(cos A - sin A))`
(cosA − sinA) + (cosA + sinA) = 2 cosA
(cosA + sinA) (cosA − sinA) = cos2A − sin2A = cos(2A)
cos(2A) = 2cos2A − 1
`(2cosA)/cos(2A) = (2cosA)/(2cos^2 A-1)`
`1/(cosA + sinA) + 1/(cosA - sinA) = (2cosA)/(2cos^2A - 1)`
APPEARS IN
RELATED QUESTIONS
Prove the following trigonometric identities.
`tan theta + 1/tan theta` = sec θ.cosec θ
Prove the following trigonometric identities.
`(cos theta)/(cosec theta + 1) + (cos theta)/(cosec theta - 1) = 2 tan theta`
Prove the following identities:
`secA/(secA + 1) + secA/(secA - 1) = 2cosec^2A`
If `cosA/cosB = m` and `cosA/sinB = n`, show that : (m2 + n2) cos2 B = n2.
Show that none of the following is an identity:
`tan^2 theta + sin theta = cos^2 theta`
Prove the following identity :
`(cosecA - sinA)(secA - cosA)(tanA + cotA) = 1`
Prove that: `cos^2 A + 1/(1 + cot^2 A) = 1`.
If tan θ + cot θ = 2, then tan2θ + cot2θ = ?
Prove that sin θ (1 – tan θ) – cos θ (1 – cot θ) = cosec θ – sec θ.
sec θ when expressed in term of cot θ, is equal to ______.
