Advertisements
Advertisements
प्रश्न
Prove the following identity :
`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (cosA + 1)/sinA`
Advertisements
उत्तर
`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (cosA + 1)/sinA`
LHS = `(cotA + cosecA - 1)/(cotA - cosecA + 1)`
we know that , cosec2A - cot2A = 1
substituting this in the numerator
`(cosecA + cotA - (cosec^2A - cot^2A))/(cotA - cosecA + 1)` .....(x²-y²= (x+y)(x-y))
`(cosecA + cotA - (cosecA + cotA)(cosecA - cotA))/(cotA - cosecA + 1)`
taking common
`((cosec A + cot A)(1-cosec A + cot A) )/ (cot A - cosec A + 1)`
cancelling like terms in numerator and denominator
we are left with cosec A + cot A
`= 1/sin A + cos A/sin A`
`= (1+cos A) / sin A`
= RHS
APPEARS IN
संबंधित प्रश्न
If m=(acosθ + bsinθ) and n=(asinθ – bcosθ) prove that m2+n2=a2+b2
(secA + tanA) (1 − sinA) = ______.
Show that `sqrt((1+cosA)/(1-cosA)) = cosec A + cot A`
Prove the following identities:
`(1 - 2sin^2A)^2/(cos^4A - sin^4A) = 2cos^2A - 1`
If sin θ = `11/61`, find the values of cos θ using trigonometric identity.
If tanθ `= 3/4` then find the value of secθ.
Prove that `(sin θ. cos (90° - θ) cos θ)/sin( 90° - θ) + (cos θ sin (90° - θ) sin θ)/(cos(90° - θ)) = 1`.
Prove that: `(sin A + cos A)/(sin A - cos A) + (sin A - cos A)/(sin A + cos A) = 2/(sin^2 A - cos^2 A)`.
cos 45° = ?
If cos 9α = sin α and 9α < 90°, then the value of tan 5α is ______.
