Advertisements
Advertisements
Question
If x = r sinA cosB , y = r sinA sinB and z = r cosA , prove that `x^2 + y^2 + z^2 = r^2`
Advertisements
Solution
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
RELATED QUESTIONS
Prove the following identities:
`(cosecA - 1)/(cosecA + 1) = (cosA/(1 + sinA))^2`
What is the value of (1 − cos2 θ) cosec2 θ?
Write True' or False' and justify your answer the following :
The value of the expression \[\sin {80}^° - \cos {80}^°\]
If a cot θ + b cosec θ = p and b cot θ − a cosec θ = q, then p2 − q2
Prove the following identity :
( 1 + cotθ - cosecθ) ( 1 + tanθ + secθ)
Prove the following identity:
tan2A − sin2A = tan2A · sin2A
Prove the following identity :
`(cosecA - sinA)(secA - cosA)(tanA + cotA) = 1`
If secθ + tanθ = m , secθ - tanθ = n , prove that mn = 1
Without using trigonometric table , evaluate :
`sin72^circ/cos18^circ - sec32^circ/(cosec58^circ)`
Prove that
`(cot "A" + "cosec A" - 1)/(cot"A" - "cosec A" + 1) = (1 + cos "A")/"sin A"`
