Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
Prove that (cosec A – sin A)(sec A – cos A) sec2 A = tan A.
Prove that:
Sin4θ - cos4θ = 1 - 2cos2θ
Write True' or False' and justify your answer the following :
The value of sin θ+cos θ is always greater than 1 .
Prove the following identity :
sinθcotθ + sinθcosecθ = 1 + cosθ
Without using trigonometric identity , show that :
`tan10^circ tan20^circ tan30^circ tan70^circ tan80^circ = 1/sqrt(3)`
Without using trigonometric identity , show that :
`sin(50^circ + θ) - cos(40^circ - θ) = 0`
Prove that: `(sec θ - tan θ)/(sec θ + tan θ ) = 1 - 2 sec θ.tan θ + 2 tan^2θ`
If x = a tan θ and y = b sec θ then
If tan θ + cot θ = 2, then tan2θ + cot2θ = ?
Factorize: sin3θ + cos3θ
Hence, prove the following identity:
`(sin^3θ + cos^3θ)/(sin θ + cos θ) + sin θ cos θ = 1`
