Advertisements
Advertisements
प्रश्न
Prove the following identities.
`(sin^3"A" + cos^3"A")/(sin"A" + cos"A") + (sin^3"A" - cos^3"A")/(sin"A" - cos"A")` = 2
Advertisements
उत्तर
`(sin^3"A" + cos^3"A")/(sin"A" + cos"A") + (sin^3"A" - cos^3"A")/(sin"A" - cos"A")` = 2
L.H.S = `(sin^3"A" + cos^3"A")/(sin"A" + cos"A") + (sin^3"A" - cos^3"A")/(sin"A" - cos"A")`
= `((sin"A" + cos"A")(sin^2"A" - sin"A"cos"A" + cos^2"A"))/((sin"A" + cos"A")) + ((sin"A" - cos"A")(sin^2"A" + sin"A"cos"A" + cos^2"A"))/((sin"A" - cos"A"))`
= (sin2 A + cos2 A) − sin A cos A + (sin2 A + cos2 A) + sin A cos A
= 1 + 1
= 2
L.H.S = R.H.S
∴`(sin^3"A" + cos^3"A")/(sin"A" + cos"A") + (sin^3"A" - cos^3"A")/(sin"A" - cos"A")` = 2
APPEARS IN
संबंधित प्रश्न
9 sec2 A − 9 tan2 A = ______.
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 trigonometric identities.
`(cot^2 A(sec A - 1))/(1 + sin A) = sec^2 A ((1 - sin A)/(1 + sec A))`
Prove that:
`(sinA - sinB)/(cosA + cosB) + (cosA - cosB)/(sinA + sinB) = 0`
If x = r cos A cos B, y = r cos A sin B and z = r sin A, show that : x2 + y2 + z2 = r2
Prove the following identity :
`sqrt(cosec^2q - 1) = "cosq cosecq"`
Prove the following identity :
`(1 + tan^2A) + (1 + 1/tan^2A) = 1/(sin^2A - sin^4A)`
Prove the following identity :
`(1 + cotA + tanA)(sinA - cosA) = secA/(cosec^2A) - (cosecA)/sec^2A`
Given `cos38^circ sec(90^circ - 2A) = 1` , Find the value of <A
If (sin α + cosec α)2 + (cos α + sec α)2 = k + tan2α + cot2α, then the value of k is equal to
