Advertisements
Advertisements
प्रश्न
Prove the following identity :
`(cotA + tanB)/(cotB + tanA) = cotAtanB`
उत्तर
`(cotA + tanB)/(cotB + tanA) = cotAtanB`
`(cotA + tanB)/(cotB + tanA)`
= `(1/tanA + tanB)/(1/tanB + tanA)`
= `((1 + tanAtanB)/tanA)/((1 + tanAtanB)/tanB) = (1 + tanAtanB)/tanA.tanB/(1 + tanAtanB)`
= `tanB/tanA = 1/tanA.tanB = cotAtanB`
APPEARS IN
संबंधित प्रश्न
If sinθ + sin2 θ = 1, prove that cos2 θ + cos4 θ = 1
Prove the following trigonometric identities.
`cosec theta sqrt(1 - cos^2 theta) = 1`
Prove the following trigonometric identities.
sin2 A cot2 A + cos2 A tan2 A = 1
`(tan theta)/((sec theta -1))+(tan theta)/((sec theta +1)) = 2 sec theta`
`(sin theta)/((sec theta + tan theta -1)) + cos theta/((cosec theta + cot theta -1))=1`
Prove that:
`"tan A"/(1 + "tan"^2 "A")^2 + "Cot A"/(1 + "Cot"^2 "A")^2 = "sin A cos A"`.
Prove the following identity :
`cosec^4A - cosec^2A = cot^4A + cot^2A`
Prove the following identity :
`(1 + cotA + tanA)(sinA - cosA) = secA/(cosec^2A) - (cosecA)/sec^2A`
Without using a trigonometric table, prove that
`(cos 70°)/(sin 20°) + (cos 59°)/(sin 31°) - 8sin^2 30° = 0`.
sin(45° + θ) – cos(45° – θ) is equal to ______.
