Advertisements
Advertisements
Question
Prove that `sqrt((1 + sin θ)/(1 - sin θ))` = sec θ + tan θ.
Advertisements
Solution
LHS = `sqrt((1 + sin θ)/(1 - sin θ) xx (1 + sin θ)/(1 + sin θ))`
= `sqrt((1 + sin θ)^2/(1 - sin^2θ))`
= `sqrt((1 + sin θ)^2/(cos^2θ)`
= `(1 + sin θ)/cos θ = 1/cos θ + sin θ/cos θ`
= sec θ + tan θ
= RHS
Hence proved.
RELATED QUESTIONS
Prove that: `(1 – sinθ + cosθ)^2 = 2(1 + cosθ)(1 – sinθ)`
Prove the following trigonometric identities.
`(1/(sec^2 theta - cos theta) + 1/(cosec^2 theta - sin^2 theta)) sin^2 theta cos^2 theta = (1 - sin^2 theta cos^2 theta)/(2 + sin^2 theta + cos^2 theta)`
Prove the following identities:
`cosecA + cotA = 1/(cosecA - cotA)`
Prove that:
`"tanθ"/("secθ" – 1) = (tanθ + secθ + 1)/(tanθ + secθ - 1)`
Prove that:
tan (55° + x) = cot (35° – x)
Prove that:
`sqrt((sectheta - 1)/(sec theta + 1)) + sqrt((sectheta + 1)/(sectheta - 1)) = 2cosectheta`
Without using trigonometric table, prove that
`cos^2 26° + cos 64° sin 26° + (tan 36°)/(cot 54°) = 2`
If tan θ = `13/12`, then cot θ = ?
Prove that cot2θ × sec2θ = cot2θ + 1
If 2 cos θ + sin θ = `1(θ ≠ π/2)`, then 7 cos θ + 6 sin θ is equal to ______.
