Advertisements
Advertisements
Question
If 3 `cot theta = 4 , "write the value of" ((2 cos theta - sin theta))/(( 4 cos theta - sin theta))`
Advertisements
Solution
W e have ,
3 `cot theta = 4 `
⇒ ` cot theta = 4/3 `
Now,
`((2 cos theta + sin theta ))/((4 cos theta - sin theta))`
=` (((2 cos theta )/ sin theta + sin theta / sin theta))/(((4 cos theta) / sin theta - sin theta/ sin theta))` (๐ท๐๐ฃ๐๐๐๐๐ ๐๐ข๐๐๐๐๐ก๐๐ ๐๐๐ ๐๐๐๐๐๐๐๐๐ก๐๐ ๐๐ฆ sin ๐)
=`((2 cot theta +1))/((4 cot theta -1))`
=`((2xx4/3 +1))/((4xx4/3-1))`
=`((8/3+1/1))/((16/3-1/1))`
=`(((8+3)/3))/(((16-3)/3))`
=`((11/3))/((13/3))`
=`11/13`
APPEARS IN
RELATED QUESTIONS
Prove the following trigonometric identities:
(i) (1 – sin2θ) sec2θ = 1
(ii) cos2θ (1 + tan2θ) = 1
Prove the following identities:
`(i) (sinθ + cosecθ)^2 + (cosθ + secθ)^2 = 7 + tan^2 θ + cot^2 θ`
`(ii) (sinθ + secθ)^2 + (cosθ + cosecθ)^2 = (1 + secθ cosecθ)^2`
`(iii) sec^4 θ– sec^2 θ = tan^4 θ + tan^2 θ`
If tanθ + sinθ = m and tanθ – sinθ = n, show that `m^2 – n^2 = 4\sqrt{mn}.`
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(cosec θ – cot θ)^2 = (1-cos theta)/(1 + cos theta)`
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`cos A/(1 + sin A) + (1 + sin A)/cos A = 2 sec A`
Prove that `(sin theta)/(1-cottheta) + (cos theta)/(1 - tan theta) = cos theta + sin theta`
Prove the following trigonometric identities.
(sec2 θ − 1) (cosec2 θ − 1) = 1
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 x = a sec θ + b tan θ and y = a tan θ + b sec θ, prove that x2 − y2 = a2 − b2
Prove the following identities:
`(secA - tanA)/(secA + tanA) = 1 - 2secAtanA + 2tan^2A`
Show that : `sinAcosA - (sinAcos(90^circ - A)cosA)/sec(90^circ - A) - (cosAsin(90^circ - A)sinA)/(cosec(90^circ - A)) = 0`
Prove that:
(cosec A – sin A) (sec A – cos A) sec2 A = tan A
Prove the following identity :
`(cotA + tanB)/(cotB + tanA) = cotAtanB`
Prove the following Identities :
`(cosecA)/(cotA+tanA)=cosA`
If secθ + tanθ = m , secθ - tanθ = n , prove that mn = 1
If A = 60°, B = 30° verify that tan( A - B) = `(tan A - tan B)/(1 + tan A. tan B)`.
If `sec θ + tan θ = sqrt(3)`, complete the activity to find the value of sec θ – tan θ.
Activity:
`square = 1 + tan^2θ` ...[Fundamental trigonometric identity]
`square - tan^2θ = 1`
`(sec θ + tan θ) . (sec θ - tan θ) = square`
`sqrt(3) . (sec θ - tan θ) = 1`
`(sec θ - tan θ) = square`
Prove that sec2θ + cosec2θ = sec2θ × cosec2θ.
Prove that sin4A – cos4A = 1 – 2 cos2A.
