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महाराष्ट्र राज्य शिक्षण मंडळएस.एस.सी (इंग्रजी माध्यम) इयत्ता १० वी

If tan θ = 13/12, then cot θ = ?

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प्रश्न

If `tan θ = 13/12`, then cot θ = ?

बेरीज
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उत्तर

 `cot θ = 1/(tan θ)`

= `1/(13/12)`

∴ `cot θ = 12/13`

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पाठ 6: Trigonometry - Exercise

संबंधित प्रश्‍न

Prove the following trigonometric identities:

`(\text{i})\text{ }\frac{\sin \theta }{1-\cos \theta }=\text{cosec}\theta+\cot \theta `


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 trigonometric identities.

`(cot A - cos A)/(cot A + cos A) = (cosec A - 1)/(cosec A + 1)`


Prove that:

(1 + tan A . tan B)2 + (tan A – tan B)2 = sec2 A sec2 B


`1+((tan^2 theta) cot theta)/(cosec^2 theta) = tan theta`


`sqrt((1 + sin θ)/(1 - sin θ)) = sec θ + tan θ`


\[\frac{\sin \theta}{1 + \cos \theta}\]is equal to 


Prove the following identity:

`cosA/(1 + sinA) = secA - tanA`


Prove the following identity :

`tanA - cotA = (1 - 2cos^2A)/(sinAcosA)`


Evaluate:

sin2 34° + sin2 56° + 2 tan 18° tan 72° – cot2 30°


If x = r sin θ cos Φ, y = r sin θ sin Φ and z = r cos θ, prove that x2 + y2 + z2 = r2. 


Prove that `((1 + sin θ - cos θ)/( 1 + sin θ + cos θ))^2 = (1 - cos θ)/(1 + cos θ)`.


If A + B = 90°, show that `(sin B + cos A)/sin A = 2tan B + tan A.`


Prove the following identities.

`(1 - tan^2theta)/(cot^2 theta - 1)` = tan2 θ


Prove the following identities.

`sqrt((1 + sin theta)/(1 - sin theta)) + sqrt((1 - sin theta)/(1 + sin theta))` = 2 sec θ


If (sin α + cosec α)2 + (cos α + sec α)2 = k + tan2α + cot2α, then the value of k is equal to


Prove the following:

`1 + (cot^2 alpha)/(1 + "cosec"  alpha)` = cosec α


Show that tan4θ + tan2θ = sec4θ – sec2θ.


If sin θ + cos θ = p and sec θ + cosec θ = q, then prove that q(p2 – 1) = 2p.


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