Advertisements
Advertisements
प्रश्न
Prove that `(cosθ)/(1 + sinθ) = (1 - sinθ)/(cosθ)`.
Advertisements
उत्तर
L.H.S. = `(cosθ)/(1 + sinθ)`
= `(cosθ)/(1 + sinθ) xx (1 - sinθ)/(1 - sinθ)` ...[On rationalising the denominator]
= `(cosθ(1 - sinθ))/(1 - sin^2θ)`
= `(cosθ(1 - sinθ))/(cos^2θ)` ...`[(∵ sin^2θ + cos^2θ = 1),(∴ 1 -sin^2θ = cos^2θ)]`
= `(1 - sinθ)/(cosθ)`
= R.H.S.
∴ `(cosθ)/(1 + sinθ) = (1 - sinθ)/(cosθ)`
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
tan2θ cos2θ = 1 − cos2θ
Prove the following trigonometric identities.
`(1 - sin θ)/(1 + sin θ) = (sec θ - tan θ)^2`
Prove the following trigonometric identities.
`sin A/(sec A + tan A - 1) + cos A/(cosec A + cot A + 1) = 1`
Prove the following identities:
`((1 + tan^2A)cotA)/(cosec^2A) = tan A`
If m = a sec A + b tan A and n = a tan A + b sec A, then prove that : m2 – n2 = a2 – b2
Prove the following identities:
`sinA/(1 - cosA) - cotA = cosecA`
Prove that:
`(sinA - cosA)(1 + tanA + cotA) = secA/(cosec^2A) - (cosecA)/(sec^2A)`
`sin^6 theta + cos^6 theta =1 -3 sin^2 theta cos^2 theta`
`(cot ^theta)/((cosec theta+1)) + ((cosec theta + 1))/cot theta = 2 sec theta`
`sqrt((1-cos theta)/(1+cos theta)) = (cosec theta - cot theta)`
Write the value of `(sin^2 theta 1/(1+tan^2 theta))`.
Write the value of sin A cos (90° − A) + cos A sin (90° − A).
If x = a sec θ and y = b tan θ, then b2x2 − a2y2 =
prove that `1/(1 + cos(90^circ - A)) + 1/(1 - cos(90^circ - A)) = 2cosec^2(90^circ - A)`
Given `cos38^circ sec(90^circ - 2A) = 1` , Find the value of <A
Prove that : `(sin(90° - θ) tan(90° - θ) sec (90° - θ))/(cosec θ. cos θ. cot θ) = 1`
Prove that `((1 - cos^2 θ)/cos θ)((1 - sin^2θ)/(sin θ)) = 1/(tan θ + cot θ)`
If x = h + a cos θ, y = k + b sin θ.
Prove that `((x - h)/a)^2 + ((y - k)/b)^2 = 1`.
sin4A – cos4A = 1 – 2cos2A. For proof of this complete the activity given below.
Activity:
L.H.S. = `square`
= (sin2A + cos2A) `(square)`
= `1 (square)` ...`[sin^2"A" + square = 1]`
= `square` – cos2A ...[sin2A = 1 – cos2A]
= `square`
= R.H.S.
Prove that `(sin θ + "cosec" θ)/(sin θ) = 2 + cot^2θ`.
