Advertisements
Advertisements
प्रश्न
Prove the following identities:
`cosecA + cotA = 1/(cosecA - cotA)`
Advertisements
उत्तर
L.H.S. = `cosecA + cotA`
= `(cosecA + cotA)/1 xx (cosecA - cotA)/(cosecA - cotA)`
= `(cosec^2A - cot^2A)/(cosecA - cotA)`
= `(1 + cot^2A - cot^2A)/(cosecA - cotA)`
= `1/(cosecA - cotA)` = R.H.S.
APPEARS IN
संबंधित प्रश्न
If `x/a=y/b = z/c` show that `x^3/a^3 + y^3/b^3 + z^3/c^3 = (3xyz)/(abc)`.
Prove the following trigonometric identities.
`1/(sec A - 1) + 1/(sec A + 1) = 2 cosec A cot A`
Prove the following identities:
`(sinA + cosA)/(sinA - cosA) + (sinA - cosA)/(sinA + cosA) = 2/(2sin^2A - 1)`
`(sin theta+1-cos theta)/(cos theta-1+sin theta) = (1+ sin theta)/(cos theta)`
`{1/((sec^2 theta- cos^2 theta))+ 1/((cosec^2 theta - sin^2 theta))} ( sin^2 theta cos^2 theta) = (1- sin^2 theta cos ^2 theta)/(2+ sin^2 theta cos^2 theta)`
Write the value of `cosec^2 theta (1+ cos theta ) (1- cos theta).`
If x = a sin θ and y = b cos θ, what is the value of b2x2 + a2y2?
If cosec θ = 2x and \[5\left( x^2 - \frac{1}{x^2} \right)\] \[2\left( x^2 - \frac{1}{x^2} \right)\]
Prove the following identity :
`sinA/(1 + cosA) + (1 + cosA)/sinA = 2cosecA`
If cos A = `(2sqrt(m))/(m + 1)`, then prove that cosec A = `(m + 1)/(m - 1)`.
