Advertisements
Advertisements
प्रश्न
If x = r sin A cos B, y = r sin A sin B and z = r cos A, then prove that : x2 + y2 + z2 = r2
Advertisements
उत्तर
L.H.S. = x2 + y2 + z2
= (r sin A cos B)2 + (r sin A sin B)2 + (r cos A)2
= r2 sin2 A cos2 B + r2 sin2 A sin2 B + r2 cos2 A
= r2 sin2 A (cos2 B + sin2 B) + r2 cos2 A
= r2 (sin2 A + cos2 A)
= r2 = R.H.S.
APPEARS IN
संबंधित प्रश्न
The angles of depression of two ships A and B as observed from the top of a light house 60 m high are 60° and 45° respectively. If the two ships are on the opposite sides of the light house, find the distance between the two ships. Give your answer correct to the nearest whole number.
If `x/a=y/b = z/c` show that `x^3/a^3 + y^3/b^3 + z^3/c^3 = (3xyz)/(abc)`.
Prove the following trigonometric identities.
(sec2 θ − 1) (cosec2 θ − 1) = 1
Prove the following trigonometric identities.
`(cot^2 A(sec A - 1))/(1 + sin A) = sec^2 A ((1 - sin A)/(1 + sec A))`
Prove the following identities:
cosec A(1 + cos A) (cosec A – cot A) = 1
(cosec θ − sin θ) (sec θ − cos θ) (tan θ + cot θ) is equal to
If sinA + cosA = m and secA + cosecA = n , prove that n(m2 - 1) = 2m
If x = h + a cos θ, y = k + b sin θ.
Prove that `((x - h)/a)^2 + ((y - k)/b)^2 = 1`.
If `sec θ = 41/40`, then find values of sin θ, cot θ, cosec θ.
If sinA + sin2A = 1, then the value of the expression (cos2A + cos4A) is ______.
