Advertisements
Advertisements
рдкреНрд░рд╢реНрди
If 3 `cot theta = 4 , "write the value of" ((2 cos theta - sin theta))/(( 4 cos theta - sin theta))`
Advertisements
рдЙрддреНрддрд░
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))` (ЁЭР╖ЁЭСЦЁЭСгЁЭСЦЁЭССЁЭСЦЁЭСЫЁЭСФ ЁЭСЫЁЭСвЁЭСЪЁЭСТЁЭСЯЁЭСОЁЭСбЁЭСЬЁЭСЯ ЁЭСОЁЭСЫЁЭСС ЁЭССЁЭСТЁЭСЫЁЭСЬЁЭСЪЁЭСЦЁЭСЫЁЭСОЁЭСбЁЭСЬЁЭСЯ ЁЭСПЁЭСж sin ЁЭЬГ)
=`((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
рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНтАНрди
Prove the following trigonometric identities.
`cos A/(1 - tan A) + sin A/(1 - cot A) = sin A + cos A`
Prove the following trigonometric identities.
`(cot A - cos A)/(cot A + cos A) = (cosec A - 1)/(cosec A + 1)`
Prove the following trigonometric identities.
`[tan θ + 1/cos θ]^2 + [tan θ - 1/cos θ]^2 = 2((1 + sin^2 θ)/(1 - sin^2 θ))`
Prove the following trigonometric identities.
`(1 + cot A + tan A)(sin A - cos A) = sec A/(cosec^2 A) - (cosec A)/sec^2 A = sin A tan A - cos A cot A`
If sin A + cos A = p and sec A + cosec A = q, then prove that : q(p2 – 1) = 2p.
Prove that:
`cosA/(1 + sinA) = secA - tanA`
`(tan^2theta)/((1+ tan^2 theta))+ cot^2 theta/((1+ cot^2 theta))=1`
`(1-tan^2 theta)/(cot^2-1) = tan^2 theta`
`(1+ cos theta + sin theta)/( 1+ cos theta - sin theta )= (1+ sin theta )/(cos theta)`
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 :
`(tanθ + 1/cosθ)^2 + (tanθ - 1/cosθ)^2 = 2((1 + sin^2θ)/(1 - sin^2θ))`
prove that `1/(1 + cos(90^circ - A)) + 1/(1 - cos(90^circ - A)) = 2cosec^2(90^circ - A)`
Prove that `tan^3 θ/( 1 + tan^2 θ) + cot^3 θ/(1 + cot^2 θ) = sec θ. cosec θ - 2 sin θ cos θ.`
Choose the correct alternative:
Which is not correct formula?
If tan θ + cot θ = 2, then tan2θ + cot2θ = ?
Prove that 2(sin6A + cos6A) – 3(sin4A + cos4A) + 1 = 0
If `sqrt(3) tan θ` = 1, then find the value of sin2θ – cos2θ.
Simplify (1 + tan2θ)(1 – sinθ)(1 + sinθ)
If cot θ = `40/9`, find the values of cosec θ and sinθ,
We have, 1 + cot2θ = cosec2θ
1 + `square` = cosec2θ
1 + `square` = cosec2θ
`(square + square)/square` = cosec2θ
`square/square` = cosec2θ ......[Taking root on the both side]
cosec θ = `41/9`
and sin θ = `1/("cosec" θ)`
sin θ = `1/square`
∴ sin θ = `9/41`
The value is cosec θ = `41/9`, and sin θ = `9/41`
Prove that `(cot A - cos A)/(cot A + cos A) = (cos^2 A)/(1 + sin A)^2`
