Advertisements
Advertisements
प्रश्न
Prove the following identity :
cosecθ(1 + cosθ)(cosecθ - cotθ) = 1
उत्तर
LHS = cosecθ(1 + cosθ)(cosecθ - cotθ)
= `1/sinθ(1 + cosθ)(1/sinθ - cosθ/sinθ)`
= `((1 + cosθ))/sinθ ((1-cosθ)/sinθ)`
= `(1 - cos^2θ)/sin^2θ = sin^2θ/sin^2θ = 1 = RHS`
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
(cosec θ − sec θ) (cot θ − tan θ) = (cosec θ + sec θ) ( sec θ cosec θ − 2)
Prove that
`sqrt((1 + sin θ)/(1 - sin θ)) + sqrt((1 - sin θ)/(1 + sin θ)) = 2 sec θ`
Write the value of `(sin^2 theta 1/(1+tan^2 theta))`.
Eliminate θ, if
x = 3 cosec θ + 4 cot θ
y = 4 cosec θ – 3 cot θ
If 5x = sec θ and \[\frac{5}{x} = \tan \theta\]find the value of \[5\left( x^2 - \frac{1}{x^2} \right)\]
Find A if tan 2A = cot (A-24°).
Prove that `(sin (90° - θ))/cos θ + (tan (90° - θ))/cot θ + (cosec (90° - θ))/sec θ = 3`.
If x sin3 θ + y cos3 θ = sin θ cos θ and x sin θ = y cos θ, then prove that x2 + y2 = 1
Prove that
`(cot "A" + "cosec A" - 1)/(cot"A" - "cosec A" + 1) = (1 + cos "A")/"sin A"`
(sec2 θ – 1) (cosec2 θ – 1) is equal to ______.
