हिंदी

tan (90 – θ) = ? A) sin θ B) cos θ C) cot θ D) tan θ

Advertisements
Advertisements

प्रश्न

tan (90 – θ) = ?

विकल्प

  • sin θ

  • cos θ

  • cot θ

  • tan θ

MCQ
Advertisements

उत्तर

cot θ

Explanation:

tan(90° – θ)

= `sin(90^circ - θ)/cos(90^circ - θ)`

= `(cos θ)/(sin θ)`

= cot θ

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 6: Trigonometry - Exercise

संबंधित प्रश्न

If (secA + tanA)(secB + tanB)(secC + tanC) = (secA – tanA)(secB – tanB)(secC – tanC) prove that each of the side is equal to ±1. We have,


Prove the following trigonometric identities:

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


Prove the following trigonometric identities.

`cos A/(1 - tan A) + sin A/(1 - cot A)  = sin A + cos A`


If x = a sec θ cos ϕ, y = b sec θ sin ϕ and z = c tan θ, show that `x^2/a^2 + y^2/b^2 - z^2/c^2 = 1`


Prove the following identities:

`(cosecA - 1)/(cosecA + 1) = (cosA/(1 + sinA))^2`


Prove the following identities:

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


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


If sec A + tan A = p, show that:

`sin A = (p^2 - 1)/(p^2 + 1)`


Write the value of ` sin^2 theta cos^2 theta (1+ tan^2 theta ) (1+ cot^2 theta).`


If x = r sin θ cos ϕ, y = r sin θ sin ϕ and z = r cos θ, then 


Prove the following identity :

`(cotA + tanB)/(cotB + tanA) = cotAtanB`


Prove the following identity : 

`1/(cosA + sinA - 1) + 2/(cosA + sinA + 1) = cosecA + secA`


Prove the following identity : 

`(1 + tan^2θ)sinθcosθ = tanθ`


Prove that:

`(cot A - 1)/(2 - sec^2 A) = cot A/(1 + tan A)` 


Prove that: 2(sin6 θ + cos6 θ) – 3 (sin4 θ + cos4 θ) + 1 = 0.


Prove that sec θ. cosec (90° - θ) - tan θ. cot( 90° - θ ) = 1.


If sec θ = `25/7`, find the value of tan θ.

Solution:

1 + tan2 θ = sec2 θ

∴ 1 + tan2 θ = `(25/7)^square`

∴ tan2 θ = `625/49 - square`

= `(625 - 49)/49`

= `square/49`

∴ tan θ = `square/7` ........(by taking square roots)


If 1 + sin2α = 3 sinα cosα, then values of cot α are ______.


Show that `(cos^2(45^circ + θ) + cos^2(45^circ - θ))/(tan(60^circ + θ) tan(30^circ - θ)) = 1`.


Complete the following activity to prove:

cotθ + tanθ = cosecθ × secθ

Activity: L.H.S. = cotθ + tanθ

= `cosθ/sinθ + square/cosθ`

= `(square + sin^2theta)/(sinθ xx cosθ)`

= `1/(sinθ xx  cosθ)` ....... ∵ `square`

= `1/sinθ xx 1/cosθ`

= `square xx secθ`

∴ L.H.S. = R.H.S.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×