Advertisements
Advertisements
Question
Prove the following identity :
`(cotA - cosecA)^2 = (1 - cosA)/(1 + cosA)`
Advertisements
Solution
LHS = `(cotA - cosecA)^2`
= `[cosA/sinA - 1/sinA]^2`
= `[(cosA - 1)/sinA]^2`
= `(cosA - 1)^2/sin^2A = (cosA - 1)^2/(1 - cos^2A)`
= `(-(1 - cosA))^2/((1 - cosA)(1 + cosA)) = ((1 - cosA)(1 - cosA))/((1 - cosA)(1 + cosA))`
= `(1 - cosA)/(1 + cosA)`
APPEARS IN
RELATED QUESTIONS
Prove that (1 + cot θ – cosec θ)(1+ tan θ + sec θ) = 2
Prove the following trigonometric identities.
sec A (1 − sin A) (sec A + tan A) = 1
Prove the following trigonometric identity:
`sqrt((1 + sin A)/(1 - sin A)) = sec A + tan A`
Prove the following identities:
(cosec A + sin A) (cosec A – sin A) = cot2 A + cos2 A
If x = r cos A cos B, y = r cos A sin B and z = r sin A, show that : x2 + y2 + z2 = r2
`cot^2 theta - 1/(sin^2 theta ) = -1`a
Prove the following identity :
`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (cosA + 1)/sinA`
If secθ + tanθ = m , secθ - tanθ = n , prove that mn = 1
There are two poles, one each on either bank of a river just opposite to each other. One pole is 60 m high. From the top of this pole, the angle of depression of the top and foot of the other pole are 30° and 60° respectively. Find the width of the river and height of the other pole.
Prove the following identities.
`(sin "A" - sin "B")/(cos "A" + cos "B") + (cos "A" - cos "B")/(sin "A" + sin "B")`
