Advertisements
Advertisements
प्रश्न
If x = a sin θ and y = bcos θ , write the value of`(b^2 x^2 + a^2 y^2)`
उत्तर
`(b^2 x^2 + a^2 y^2)`
=`b^2 (a sin theta )^2 + a^2 ( bcos theta)^2`
=`b^2 a^2 sin^2 theta + a^2 b^2 cos^2 theta`
=`a^2 b^2 ( sin^2 theta + cos ^2 theta)`
=`a^2 b^2 (1)`
=`a^2 b^2`
APPEARS IN
संबंधित प्रश्न
Prove the following identities:
`(i) cos4^4 A – cos^2 A = sin^4 A – sin^2 A`
`(ii) cot^4 A – 1 = cosec^4 A – 2cosec^2 A`
`(iii) sin^6 A + cos^6 A = 1 – 3sin^2 A cos^2 A.`
If m=(acosθ + bsinθ) and n=(asinθ – bcosθ) prove that m2+n2=a2+b2
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.
Prove the following trigonometric identities.
`(1 + sec theta)/sec theta = (sin^2 theta)/(1 - cos theta)`
Prove the following trigonometric identities.
`(tan^3 theta)/(1 + tan^2 theta) + (cot^3 theta)/(1 + cot^2 theta) = sec theta cosec theta - 2 sin theta cos theta`
Prove the following trigonometric identities.
if `T_n = sin^n theta + cos^n theta`, prove that `(T_3 - T_5)/T_1 = (T_5 - T_7)/T_3`
If sin θ + cos θ = x, prove that `sin^6 theta + cos^6 theta = (4- 3(x^2 - 1)^2)/4`
Prove the following identities:
cosec4 A – cosec2 A = cot4 A + cot2 A
If m = a sec A + b tan A and n = a tan A + b sec A, then prove that : m2 – n2 = a2 – b2
If sin A + cos A = m and sec A + cosec A = n, show that : n (m2 – 1) = 2 m
Prove the following identity :
`sec^4A - sec^2A = sin^2A/cos^4A`
Prove the following identity :
`(cos^3θ + sin^3θ)/(cosθ + sinθ) + (cos^3θ - sin^3θ)/(cosθ - sinθ) = 2`
Given `cos38^circ sec(90^circ - 2A) = 1` , Find the value of <A
Prove the following identities:
`1/(sin θ + cos θ) + 1/(sin θ - cos θ) = (2sin θ)/(1 - 2 cos^2 θ)`.
Choose the correct alternative:
cos θ. sec θ = ?
Choose the correct alternative:
sin θ = `1/2`, then θ = ?
If cos A = `(2sqrt("m"))/("m" + 1)`, then prove that cosec A = `("m" + 1)/("m" - 1)`
sin(45° + θ) – cos(45° – θ) is equal to ______.
If tan θ = `x/y`, then cos θ is equal to ______.
