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)`
RELATED QUESTIONS
Prove the following trigonometric identities.
`(1 + sec theta)/sec theta = (sin^2 theta)/(1 - cos theta)`
Prove the following identities:
`(sintheta - 2sin^3theta)/(2cos^3theta - costheta) = tantheta`
\[\frac{1 + \tan^2 A}{1 + \cot^2 A}\]is equal to
Prove the following identity :
`(1 - cos^2θ)sec^2θ = tan^2θ`
Prove that: 2(sin6θ + cos6θ) - 3 ( sin4θ + cos4θ) + 1 = 0.
Prove that `sqrt((1 + sin θ)/(1 - sin θ))` = sec θ + tan θ.
Without using trigonometric table, prove that
`cos^2 26° + cos 64° sin 26° + (tan 36°)/(cot 54°) = 2`
Prove the following identities.
sec6 θ = tan6 θ + 3 tan2 θ sec2 θ + 1
If sin θ + sin2 θ = 1 show that: cos2 θ + cos4 θ = 1
Choose the correct alternative:
sin θ = `1/2`, then θ = ?
