Advertisements
Advertisements
प्रश्न
Eliminate θ from the following:
x = 3secθ , y = 4tanθ
Advertisements
उत्तर
x = 3sec θ and y = 4tan θ
∴ sec θ = `x/3 and tan theta = y/4`
We know that,
sec2θ – tan2θ = 1
∴ `(x/3)^2 - (y/4)^2` = 1
∴ `x^2/9 - y^2/16` = 1
∴ `(16x^2 - 9y^2)/(16 xx 9)` = 1
∴ `(16x^2 - 9y^2)/144` = 1
∴ 16x2 − 9y2 = 1 x 144
∴ 16x2 – 9y2 = 144
APPEARS IN
संबंधित प्रश्न
Evaluate the following:
sin 30° + cos 45° + tan 180°
Evaluate the following :
sin 30° × cos 45° × tan 360°
If tanθ = `1/2`, evaluate `(2sin theta + 3cos theta)/(4cos theta + 3sin theta)`
Eliminate θ from the following :
x = 6cosecθ, y = 8cotθ
Eliminate θ from the following :
x = 4cosθ − 5sinθ, y = 4sinθ + 5cosθ
Eliminate θ from the following :
x = 5 + 6cosecθ, y = 3 + 8cotθ
Eliminate θ from the following:
2x = 3 − 4 tan θ, 3y = 5 + 3 sec θ
Find the acute angle θ such that 5tan2θ + 3 = 9secθ.
Find sinθ such that 3cosθ + 4sinθ = 4
Prove the following identities:
`(1 + tan^2 "A") + (1 + 1/tan^2"A") = 1/(sin^2 "A" - sin^4"A")`
Prove the following identities:
(cos2A – 1) (cot2A + 1) = −1
Prove the following identities:
(sinθ + sec θ)2 + (cosθ + cosec θ)2 = (1 + cosecθ sec θ)2
Prove the following identities:
`sintheta/(1 + costheta) + (1 + costheta)/sintheta` = 2cosecθ
Prove the following identity:
`tantheta/(sectheta - 1) = (sectheta + 1)/tantheta`
Prove the following identities:
(sec A + cos A)(sec A − cos A) = tan2A + sin2A
Prove the following identities:
`(1 - sectheta + tan theta)/(1 + sec theta - tan theta) = (sectheta + tantheta - 1)/(sectheta + tantheta + 1)`
Select the correct option from the given alternatives:
If θ = 60°, then `(1 + tan^2theta)/(2tantheta)` is equal to
Select the correct option from the given alternatives:
If cosecθ + cotθ = `5/2`, then the value of tanθ is
Select the correct option from the given alternatives:
`1 - sin^2theta/(1 + costheta) + (1 + costheta)/sintheta - sintheta/(1 - costheta)` equals
Select the correct option from the given alternatives:
If cosecθ − cotθ = q, then the value of cot θ is
Select the correct option from the given alternatives:
The value of tan1°.tan2°tan3°..... tan89° is equal to
Prove the following:
sin2A cos2B + cos2A sin2B + cos2A cos2B + sin2A sin2B = 1
Prove the following:
`(tan theta + 1/costheta)^2 + (tan theta - 1/costheta)^2 = 2((1 + sin^2theta)/(1 - sin^2theta))`
Prove the following:
2 sec2θ – sec4θ – 2cosec2θ + cosec4θ = cot4θ – tan4θ
Prove the following:
sin4θ + cos4θ = 1 – 2 sin2θ cos2θ
Prove the following:
sin4θ +2sin2θ . cos2θ = 1 − cos4θ
Prove the following:
`(sin^3theta + cos^3theta)/(sintheta + costheta) + (sin^3theta - cos^3theta)/(sintheta - costheta)` = 2
Prove the following:
tan2θ − sin2θ = sin4θ sec2θ
Prove the following:
(1 + tanA · tanB)2 + (tanA − tanB)2 = sec2A · sec2B
Prove the following:
`("cosec"theta + cottheta + 1)/(cottheta + "cosec" theta - 1) = cottheta/("cosec"theta - 1)`
If θ lies in the first quadrant and 5 tan θ = 4, then `(5 sin θ - 3 cos θ)/(sin θ + 2 cos θ)` is equal to ______.
