Advertisements
Advertisements
प्रश्न
Prove the following identities:
`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (1 + cosA)/sinA`
Advertisements
उत्तर
L.H.S. = `(cotA + cosecA - 1)/(cotA - cosecA + 1)`
= `(cotA + cosecA - (cosec^2A - cot^2A))/(cotA - cosecA + 1)` ...[cosec2A – cot2A = 1]
= `(cotA + cosecA - [(cosecA - cotA)(cosecA + cotA)])/(cotA - cosecA + 1`
= `(cotA + cosecA[1 - cosecA + cotA])/(cotA - cosecA + 1)`
= cot A + cosec A
= `cosA/sinA + 1/sinA`
= `(1 + cosA)/sinA`
संबंधित प्रश्न
Show that : `sinA/sin(90^circ - A) + cosA/cos(90^circ - A) = sec A cosec A`
If tan A = n tan B and sin A = m sin B, prove that `cos^2A = (m^2 - 1)/(n^2 - 1)`
`sqrt((1 + sin θ)/(1 - sin θ)) = sec θ + tan θ`
Prove the following identities:
`(1 + tan theta + cot theta)(sin theta - cos theta) = ((sec theta)/("cosec"^2 theta) - ("cosec" theta)/(sec^2 theta))`
\[\frac{1 + \tan^2 A}{1 + \cot^2 A}\]is equal to
Prove the following identity :
`sqrt((1 + sinq)/(1 - sinq)) + sqrt((1- sinq)/(1 + sinq))` = 2secq
Prove the following identity :
`1/(cosA + sinA - 1) + 2/(cosA + sinA + 1) = cosecA + secA`
Prove that: `(sin θ - 2sin^3 θ)/(2 cos^3 θ - cos θ) = tan θ`.
Prove that:
`(cos^3 θ + sin^3 θ)/(cos θ + sin θ) + (cos^3 θ - sin^3 θ)/(cos θ - sin θ) = 2`
sin(45° + θ) – cos(45° – θ) is equal to ______.
