Advertisements
Advertisements
प्रश्न
If x = r sinA cosB , y = r sinA sinB and z = r cosA , prove that `x^2 + y^2 + z^2 = r^2`
Advertisements
उत्तर
LHS = `(rsinAcosB)^2 + (rsinAsinB)^2 + (rcosA)^2`
⇒ `r^2sin^2Acos^2B + r^2sin^2Asin^2B + r^2cos^2A`
⇒ `r^2sin^2A(cos^2B + sin^2B) + r^2cos^2A`
⇒ `r^2(sin^2A + cos^2A) = r^2` = RHS
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`(1 - cos theta)/sin theta = sin theta/(1 + cos theta)`
if `x/a cos theta + y/b sin theta = 1` and `x/a sin theta - y/b cos theta = 1` prove that `x^2/a^2 + y^2/b^2 = 2`
Prove the following identities:
`sqrt((1 - cosA)/(1 + cosA)) = sinA/(1 + cosA)`
`1+ (cot^2 theta)/((1+ cosec theta))= cosec theta`
`1+(tan^2 theta)/((1+ sec theta))= sec theta`
If `( sin theta + cos theta ) = sqrt(2) , " prove that " cot theta = ( sqrt(2)+1)`.
If x = a sin θ and y = bcos θ , write the value of`(b^2 x^2 + a^2 y^2)`
Prove that `((1 + sin θ - cos θ)/( 1 + sin θ + cos θ))^2 = (1 - cos θ)/(1 + cos θ)`.
tan θ cosec2 θ – tan θ is equal to
Which of the following is true for all values of θ (0° ≤ θ ≤ 90°)?
