Advertisements
Advertisements
Question
Prove that:
`(sinA - cosA)(1 + tanA + cotA) = secA/(cosec^2A) - (cosecA)/(sec^2A)`
Solution
`(sinA - cosA)(1 + tanA + cotA)`
= `sinA + (sin^2A)/cosA + cosA - cosA - sinA - (cos^2A)/sinA`
= `(sin^2A)/cosA - (cos^2A)/sinA`
= `secA/(cosec^2A) - (cosecA)/(sec^2A)`
APPEARS IN
RELATED QUESTIONS
Prove that `sqrt(sec^2 theta + cosec^2 theta) = tan theta + cot theta`
As observed from the top of an 80 m tall lighthouse, the angles of depression of two ships on the same side of the lighthouse of the horizontal line with its base are 30° and 40° respectively. Find the distance between the two ships. Give your answer correct to the nearest meter.
Prove the following identities:
cosec A(1 + cos A) (cosec A – cot A) = 1
Prove the following identities:
`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (1 + cosA)/sinA`
Prove that:
`(tanA + 1/cosA)^2 + (tanA - 1/cosA)^2 = 2((1 + sin^2A)/(1 - sin^2A))`
Prove the following identities:
`cosA/(1 + sinA) + tanA = secA`
If `cos theta = 2/3 , "write the value of" ((sec theta -1))/((sec theta +1))`
If `asin^2θ + bcos^2θ = c and p sin^2θ + qcos^2θ = r` , prove that (b - c)(r - p) = (c - a)(q - r)
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
