Advertisements
Advertisements
Question
Prove the following identities:
`(sinAtanA)/(1 - cosA) = 1 + secA`
Advertisements
Solution
L.H.S. = `(sinAtanA)/(1 - cosA)`
= `(sinAtanA)/(1 - cosA) xx (1 + cosA)/(1 + cosA)`
= `(sinAtanA(1 + cosA))/(1 - cos^2A)`
= `(sinA sinA/cosA(1 + cosA))/sin^2A`
= `(1 + cosA)/cosA`
= `1/cosA + cosA/cosA`
= sec A + 1
= 1 + sec A = R.H.S.
RELATED QUESTIONS
If `sec alpha=2/sqrt3` , then find the value of `(1-cosecalpha)/(1+cosecalpha)` where α is in IV quadrant.
If secθ + tanθ = p, show that `(p^{2}-1)/(p^{2}+1)=\sin \theta`
Prove the following trigonometric identities
tan2 A + cot2 A = sec2 A cosec2 A − 2
Prove that:
`cot^2A/(cosecA - 1) - 1 = cosecA`
Write the value of `4 tan^2 theta - 4/ cos^2 theta`
If tanθ `= 3/4` then find the value of secθ.
If 5x = sec θ and \[\frac{5}{x} = \tan \theta\]find the value of \[5\left( x^2 - \frac{1}{x^2} \right)\]
\[\frac{\tan \theta}{\sec \theta - 1} + \frac{\tan \theta}{\sec \theta + 1}\] is equal to
If a cos θ + b sin θ = m and a sin θ − b cos θ = n, then a2 + b2 =
If sin θ (1 + sin2 θ) = cos2 θ, then prove that cos6 θ – 4 cos4 θ + 8 cos2 θ = 4
