हिंदी

If tan θ = 940, complete the activity to find the value of sec θ. Activity: sec2θ = 1 + □ ......[Fundamental trigonometric identity] sec2θ = 1 + □2 sec2θ = 1 + □ sec θ = □ - Geometry Mathematics 2

Advertisements
Advertisements

प्रश्न

If tan θ = `9/40`, complete the activity to find the value of sec θ.

Activity:

sec2θ = 1 + `square`     ......[Fundamental trigonometric identity]

sec2θ = 1 + `square^2`

sec2θ = 1 + `square` 

sec θ = `square` 

रिक्त स्थान भरें
योग

उत्तर

sec2θ = 1 + tan2θ     ......[Fundamental trigonometric identity]

∴ sec2θ = 1 + `(9/40)^2`

∴ sec2θ = 1 + `81/1600` 

∴ sec2θ = `1681/1600`

∴ sec θ = `41/40`

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 6: Trigonometry - Q.2 (A)

संबंधित प्रश्न

(1 + tan θ + sec θ) (1 + cot θ − cosec θ) = ______.


Prove the following trigonometric identities.

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


Prove the following trigonometric identities.

(sec A − cosec A) (1 + tan A + cot A) = tan A sec A − cot A cosec A


Prove the following identities:

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


`(sin theta+1-cos theta)/(cos theta-1+sin theta) = (1+ sin theta)/(cos theta)`


`{1/((sec^2 theta- cos^2 theta))+ 1/((cosec^2 theta - sin^2 theta))} ( sin^2 theta cos^2 theta) = (1- sin^2 theta cos ^2 theta)/(2+ sin^2 theta cos^2 theta)`


Show that none of the following is an identity:

`tan^2 theta + sin theta = cos^2 theta`


Write the value of tan10° tan 20° tan 70° tan 80° .


Prove that:

`"tan A"/(1 + "tan"^2 "A")^2 + "Cot A"/(1 + "Cot"^2 "A")^2 = "sin A cos A"`.


Write True' or False' and justify your answer the following: 

\[ \cos \theta = \frac{a^2 + b^2}{2ab}\]where a and b are two distinct numbers such that ab > 0.


Prove the following identity :

`sec^2A.cosec^2A = tan^2A + cot^2A + 2`


Prove the following identity :

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


Verify that the points A(–2, 2), B(2, 2) and C(2, 7) are the vertices of a right-angled triangle. 


Prove that:

`sqrt((sectheta - 1)/(sec theta + 1)) + sqrt((sectheta + 1)/(sectheta - 1)) = 2cosectheta`


Prove that: 2(sin6θ + cos6θ) - 3 ( sin4θ + cos4θ) + 1 = 0.


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


Prove the following identities.

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


Show that tan 7° × tan 23° × tan 60° × tan 67° × tan 83° = `sqrt(3)`


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


Prove that `(cot A - cos A)/(cot A + cos A) = (cos^2 A)/(1 + sin A)^2`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×