Advertisements
Advertisements
प्रश्न
If x = r cos A cos B, y = r cos A sin B and z = r sin A, show that : x2 + y2 + z2 = r2
Advertisements
उत्तर
L.H.S. = x2 + y2 + z2
= (r cos A cos B)2 + (r cos A sin B)2 + (r sin A)2
= r2 cos2 A cos2 B + r2 cos2 A sin2 B + r2 sin2 A
= r2 cos2 A (cos2 B + sin2 B) + r2 sin2 A
= r2 (cos2 A + sin2 A)
= r2 = R.H.S.
APPEARS IN
संबंधित प्रश्न
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(sin theta-2sin^3theta)/(2cos^3theta -costheta) = tan theta`
Prove the following trigonometric identities.
`cos A/(1 - tan A) + sin A/(1 - cot A) = sin A + cos A`
Prove that:
`(sinA - cosA)(1 + tanA + cotA) = secA/(cosec^2A) - (cosecA)/(sec^2A)`
`If sin theta = cos( theta - 45° ),where theta " is acute, find the value of "theta` .
Prove the following identity :
secA(1 + sinA)(secA - tanA) = 1
Prove the following identity :
`sqrt((secq - 1)/(secq + 1)) + sqrt((secq + 1)/(secq - 1))` = 2 cosesq
Prove that `sqrt((1 + sin θ)/(1 - sin θ))` = sec θ + tan θ.
If tan A + sin A = m and tan A − sin A = n, then show that `m^2 - n^2 = 4 sqrt (mn)`.
sec2θ – tan2θ = ?
If `tan θ = 7/24`, then to find value of cos θ complete the activity given below.
Activity:
sec2θ = 1 + `square` ...[Fundamental tri. identity]
sec2θ = 1 + `square^2`
sec2θ = 1 + `square/576`
sec2θ = `square/576`
sec θ = `square`
cos θ = `square` ...`[cos theta = 1/sectheta]`
