Advertisements
Advertisements
प्रश्न
If `( sin theta + cos theta ) = sqrt(2) , " prove that " cot theta = ( sqrt(2)+1)`.
Advertisements
उत्तर
We have , `(sin theta + cos theta ) = sqrt(2) cos theta`
Dividing both sides by sin θ , We get
`(sin theta)/ (sin theta )+ (cos theta)/ (sin theta)= (sqrt(2) cos theta)/ (sin theta)`
⇒ `1+ cot theta = sqrt(2) cot theta`
⇒ `sqrt(2) cot theta - cot theta =1`
⇒ `( sqrt(2) - 1 ) cot theta =1`
`⇒ cot theta = 1/ (( sqrt(2)-1))`
`⇒ cot theta = 1/((sqrt(2)-1))xx ((sqrt(2)+1))/((sqrt(2)+1))`
`⇒ cot theta = ((sqrt(2)+1))/(2-1)`
`⇒ cot theta = ((sqrt(2)+1))/1`
∴`cot theta = (sqrt (2) +1)`
APPEARS IN
संबंधित प्रश्न
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(cos A-sinA+1)/(cosA+sinA-1)=cosecA+cotA ` using the identity cosec2 A = 1 cot2 A.
Prove the following trigonometric identities.
`tan theta + 1/tan theta` = sec θ.cosec θ
Prove the following trigonometric identities.
`(cot A - cos A)/(cot A + cos A) = (cosec A - 1)/(cosec A + 1)`
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 + cot A – cosec A)(1 + tan A + sec A) = 2
Prove that:
2 sin2 A + cos4 A = 1 + sin4 A
Prove the following identities:
`((cosecA - cotA)^2 + 1)/(secA(cosecA - cotA)) = 2cotA`
If 4 cos2 A – 3 = 0, show that: cos 3 A = 4 cos3 A – 3 cos A
`(cos theta cosec theta - sin theta sec theta )/(costheta + sin theta) = cosec theta - sec theta`
Write the value of `(1 + cot^2 theta ) sin^2 theta`.
`If sin theta = cos( theta - 45° ),where theta " is acute, find the value of "theta` .
What is the value of \[\sin^2 \theta + \frac{1}{1 + \tan^2 \theta}\]
2 (sin6 θ + cos6 θ) − 3 (sin4 θ + cos4 θ) is equal to
If sec θ + tan θ = m, show that `(m^2 - 1)/(m^2 + 1) = sin theta`
`(sin A)/(1 + cos A) + (1 + cos A)/(sin A)` = 2 cosec A
Prove that: `1/(cosec"A" - cot"A") - 1/sin"A" = 1/sin"A" - 1/(cosec"A" + cot"A")`
Prove the following identities.
(sin θ + sec θ)2 + (cos θ + cosec θ)2 = 1 + (sec θ + cosec θ)2
Prove that `(cos^2θ)/(sinθ) + sin θ = "cosec" θ`.
`sqrt((1 - cos^2theta) sec^2 theta) = tan theta`
Show that tan4θ + tan2θ = sec4θ – sec2θ.
