Advertisements
Advertisements
प्रश्न
If y = `(2sinalpha)/(1 + cosalpha + sinalpha)`, then prove that `(1 - cosalpha + sinalpha)/(1 + sinalpha)` = y
उत्तर
`(2sinalpha)/(1 + cosalpha + sinalpha) = (2sinalpha)/((1 + sinalpha) + cosalpha)`
= `(2sinalpha)/((1 + sin alpha) + cos alpha) xx ((1 + sinalpha) - cosalpha)/((1 + sinalpha) - cosalpha)`
y = `(2sinalpha(1 - cosalpha + sinalpha))/((1 + sinalpha)^2 - cos^2alpha)`
= `(2sinalpha(1 - cosalpha + sinalpha))/(1 + 2sinalpha + sin^2alpha - cos^2alpha)`
= `(2sinalpha(1 - cosalpha + sinalpha))/(1 + 2sinalpha + sin^2alpha - (1 - sin^2alpha))`
= `(2sinalpha(1 - cosalpha + sinalpha))/(1 + 2sinalpha + sin^2alpha - 1 - sin^2alpha)`
= `(2sinalpha(1 - cosalpha + sinalpha))/(2sinalpha + 2sin^2alpha)`
= `(2sinalpha(1 - cosalpha + sinalpha))/(2sinalpha(1 + sinalpha))`
y = `(1 - cosalpha + sinalpha)/(1 + sinalpha)`
APPEARS IN
संबंधित प्रश्न
Identify the quadrant in which an angle given measure lies
– 230°
For each given angle, find a coterminal angle with measure of θ such that 0° ≤ θ < 360°
395°
For each given angle, find a coterminal angle with measure of θ such that 0° ≤ θ < 360°
525°
For each given angle, find a coterminal angle with measure of θ such that 0° ≤ θ < 360°
1150°
For each given angle, find a coterminal angle with measure of θ such that 0° ≤ θ < 360°
– 270°
For each given angle, find a coterminal angle with measure of θ such that 0° ≤ θ < 360°
– 450°
If a cos θ − b sin θ = c, show that a sin θ + b cos θ = `+- sqrt("a"^2 + "b"^2 - "c"^2)`
If `(cos^4α)/(cos^2β) + (sin^4α)/(sin^2β)` = 1, prove that sin4α + sin4β = 2 sin2α sin2β
If `(cos^4alpha)/(cos^2beta) + (sin^4alpha)/(sin^2beta)` = 1, prove that `(cos^4beta)/(cos^2alpha) + (sin^4beta)/(sin^2alpha)` = 1
If tan2 θ = 1 – k2, show that sec θ + tan3 θ cosec θ = (2 – k2)3/2. Also, find the values of k for which this result holds
If sec θ + tan θ = p, obtain the values of sec θ, tan θ and sin θ in terms of p
If cot θ(1 + sin θ) = 4m and cot θ(1 – sin θ) = 4n then prove that (m2 – n2)2 = m
Eliminate θ from the equations a sec θ – c tan θ = b and b sec θ + d tan θ = c
Choose the correct alternative:
The maximum value of `4sin^2x + 3cos^2x + sin x/2 + cos x/2` is
Choose the correct alternative:
Which of the following is not true?
