Advertisements
Advertisements
प्रश्न
`cosec theta (1+costheta)(cosectheta - cot theta )=1`
उत्तर
LHS = `cosec theta (1+ cos theta )( cosec theta - cot theta)`
=` (cosec theta + cosec theta xx cos theta)(cosec theta - cot theta)`
=` (cosec theta + 1/(sin theta) xx cos theta ) ( cosec theta - cot theta )`
=` ( cosec theta + cot theta )( cosec theta - cot theta)`
=` cosec^2 theta - cot^2 theta (∵ cosec^2 theta - cot^2 theta=1)`
= 1
= RHS
APPEARS IN
संबंधित प्रश्न
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(cosec θ – cot θ)^2 = (1-cos theta)/(1 + cos theta)`
if `cos theta = 5/13` where `theta` is an acute angle. Find the value of `sin theta`
Prove the following trigonometric identities.
tan2θ cos2θ = 1 − cos2θ
Prove the following trigonometric identities.
`tan theta/(1 - cot theta) + cot theta/(1 - tan theta) = 1 + tan theta + cot theta`
If x = a sec θ cos ϕ, y = b sec θ sin ϕ and z = c tan θ, show that `x^2/a^2 + y^2/b^2 - x^2/c^2 = 1`
Prove the following identities:
`(1 - cosA)/sinA + sinA/(1 - cosA)= 2cosecA`
Prove the following identities:
`(sinA - cosA + 1)/(sinA + cosA - 1) = cosA/(1 - sinA)`
Write the value of `( 1- sin ^2 theta ) sec^2 theta.`
Prove the following identity :
`2(sin^6θ + cos^6θ) - 3(sin^4θ + cos^4θ) + 1 = 0`
Prove the following identity :
`(cos^3θ + sin^3θ)/(cosθ + sinθ) + (cos^3θ - sin^3θ)/(cosθ - sinθ) = 2`
Prove that `(sin θ tan θ)/(1 - cos θ) = 1 + sec θ.`
Prove that : `(sin(90° - θ) tan(90° - θ) sec (90° - θ))/(cosec θ. cos θ. cot θ) = 1`
If x sin3θ + y cos3 θ = sin θ cos θ and x sin θ = y cos θ , then show that x2 + y2 = 1.
If 5x = sec θ and `5/x` = tan θ, then `x^2 - 1/x^2` is equal to
If x = a tan θ and y = b sec θ then
Prove that `(tan^2 theta - 1)/(tan^2 theta + 1)` = 1 – 2 cos2θ
If cosec A – sin A = p and sec A – cos A = q, then prove that `("p"^2"q")^(2/3) + ("pq"^2)^(2/3)` = 1
If tan θ + sec θ = l, then prove that sec θ = `(l^2 + 1)/(2l)`.
If a sinθ + b cosθ = c, then prove that a cosθ – b sinθ = `sqrt(a^2 + b^2 - c^2)`.
Let x1, x2, x3 be the solutions of `tan^-1((2x + 1)/(x + 1)) + tan^-1((2x - 1)/(x - 1))` = 2tan–1(x + 1) where x1 < x2 < x3 then 2x1 + x2 + x32 is equal to ______.
