Advertisements
Advertisements
प्रश्न
`(cos ec^theta + cot theta )/( cos ec theta - cot theta ) = (cosec theta + cot theta )^2 = 1+2 cot^2 theta + 2cosec theta cot theta`
Advertisements
उत्तर
Here, `( cosec theta + cot theta )/( cosec theta - cot theta)`
= `((cosec theta + cot theta) ( cosec theta + cot theta ))/(( cosec theta - cot theta ) ( cosec theta + cot theta))`
=` ((cosec theta + cot theta)^2)/(( cosec ^2 theta - cot^2 theta))`
=`((cosec theta + cot theta )^2) /1`
=`(cosec theta + cot theta )^2`
Again , `( cosec theta + cot theta )^2`
= ` cosec^2 theta + cot^2 theta + 2 cosec theta cot theta `
=` 1+cot^2 theta + cot^2 theta + 2 cosec theta cot theta (∵ cosec^2 theta - cot^2 theta =1)`
=` 1+2 cot^2 theta + 2 cosec theta cot theta `
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`(cosec A)/(cosec A - 1) + (cosec A)/(cosec A = 1) = 2 sec^2 A`
Prove the following trigonometric identities.
`cot^2 A cosec^2B - cot^2 B cosec^2 A = cot^2 A - cot^2 B`
Prove the following identities:
`1/(tan A + cot A) = cos A sin A`
Prove the following identities:
`sqrt((1 + sinA)/(1 - sinA)) = cosA/(1 - sinA)`
Prove the following identities:
sec4 A (1 – sin4 A) – 2 tan2 A = 1
` tan^2 theta - 1/( cos^2 theta )=-1`
`sin theta / ((1+costheta))+((1+costheta))/sin theta=2cosectheta`
Write the value of `(sin^2 theta 1/(1+tan^2 theta))`.
Write the value of `cosec^2 theta (1+ cos theta ) (1- cos theta).`
If `cos theta = 2/3 , "write the value of" ((sec theta -1))/((sec theta +1))`
If `sqrt(3) sin theta = cos theta and theta ` is an acute angle, find the value of θ .
Prove the following identity :
`(cotA - cosecA)^2 = (1 - cosA)/(1 + cosA)`
Prove that `( 1 + sin θ)/(1 - sin θ) = 1 + 2 tan θ/cos θ + 2 tan^2 θ` .
Prove that cosec2 (90° - θ) + cot2 (90° - θ) = 1 + 2 tan2 θ.
If x sin3θ + y cos3 θ = sin θ cos θ and x sin θ = y cos θ , then show that x2 + y2 = 1.
Prove the following identities:
`1/(sin θ + cos θ) + 1/(sin θ - cos θ) = (2sin θ)/(1 - 2 cos^2 θ)`.
Prove that `[(1 + sin theta - cos theta)/(1 + sin theta + cos theta)]^2 = (1 - cos theta)/(1 + cos theta)`
Choose the correct alternative:
cot θ . tan θ = ?
Prove that `sqrt(sec^2 theta + "cosec"^2 theta) = tan theta + cot theta`
