Advertisements
Advertisements
Question
Prove the following identities:
`sqrt((1 + sinA)/(1 - sinA)) = cosA/(1 - sinA)`
Advertisements
Solution
`sqrt((1 + sinA)/(1 - sinA))`
= `sqrt((1 + sinA)/(1 - sinA) xx (1 - sinA)/(1 - sinA))`
= `sqrt((1 - sin^2A)/(1 - sinA)^2)`
= `sqrt(cos^2A/((1 - sinA)^2)`
= `cosA/(1 - sinA)`
APPEARS IN
RELATED QUESTIONS
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(cos A-sinA+1)/(cosA+sinA-1)=cosecA+cotA ` using the identity cosec2 A = 1 cot2 A.
Prove the following trigonometric identities.
`((1 + tan^2 theta)cot theta)/(cosec^2 theta) = tan theta`
Prove the following identities:
`tan^2A - tan^2B = (sin^2A - sin^2B)/(cos^2A * cos^2B)`
Prove the following identities:
cosec4 A (1 – cos4 A) – 2 cot2 A = 1
`(1 + cot^2 theta ) sin^2 theta =1`
`(1+ tan theta + cot theta )(sintheta - cos theta) = ((sec theta)/ (cosec^2 theta)-( cosec theta)/(sec^2 theta))`
Prove that: (1+cot A - cosecA)(1 + tan A+ secA) =2.
Prove the following identities: cot θ - tan θ = `(2 cos^2 θ - 1)/(sin θ cos θ)`.
Prove that `(1 + sec A)/(sec A) = (sin^2A)/(1 - cos A)`.
If 1 + sin2α = 3 sinα cosα, then values of cot α are ______.
