Advertisements
Advertisements
प्रश्न
Prove the following identities:
`(1 + sin A)/(1 - sin A) = (cosec A + 1)/(cosec A - 1)`
उत्तर
R.H.S = `(1/(sin A) + 1)/(1/(sin A) - 1)`
= `((1 + sin A)/sin A)/((1 - sin A)/sin A)`
= `((1 + sin A))/cancelsin A xx cancelsin A/((1 - sin A))`
= `(1 + sin A)/(1 - sin A)`
∴ R.H.S = L.H.S
APPEARS IN
संबंधित प्रश्न
Prove that `sqrt(sec^2 theta + cosec^2 theta) = tan theta + cot theta`
Prove the following trigonometric identities.
`tan theta/(1 - cot theta) + cot theta/(1 - tan theta) = 1 + tan theta + cot theta`
Prove the following trigonometric identities
If x = a sec θ + b tan θ and y = a tan θ + b sec θ, prove that x2 − y2 = a2 − b2
If `cos theta = 2/3 , " write the value of" (4+4 tan^2 theta).`
Find the value of ` ( sin 50°)/(cos 40°)+ (cosec 40°)/(sec 50°) - 4 cos 50° cosec 40 °`
Prove the following identity :
`sin^2Acos^2B - cos^2Asin^2B = sin^2A - sin^2B`
If `x/(a cosθ) = y/(b sinθ) "and" (ax)/cosθ - (by)/sinθ = a^2 - b^2 , "prove that" x^2/a^2 + y^2/b^2 = 1`
Prove that `cos θ/sin(90° - θ) + sin θ/cos (90° - θ) = 2`.
Prove that
`(cot "A" + "cosec A" - 1)/(cot"A" - "cosec A" + 1) = (1 + cos "A")/"sin A"`
Prove that sin6A + cos6A = 1 – 3sin2A . cos2A
