हिंदी

Prove the Following Trigonometric Identities. Cosec Theta Sqrt(1 - Cos^2 Theta) = 1 - Mathematics

Advertisements
Advertisements

प्रश्न

Prove the following trigonometric identities.

`cosec theta sqrt(1 - cos^2 theta) = 1`

उत्तर

We know that `sin^2 theta + cos^2 theta = 1`

So,

`cosec theta sqrt(1 - cos^2 theta) = cosec theta sqrt (sin^2 theta)`

`= cosec theta sin theta`

`1/ sin theta xx sin theta`

= 1

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 11: Trigonometric Identities - Exercise 11.1 [पृष्ठ ४३]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 10
अध्याय 11 Trigonometric Identities
Exercise 11.1 | Q 4 | पृष्ठ ४३

संबंधित प्रश्न

Prove the following trigonometric identities.

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


Prove the following trigonometric identities.

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


Prove the following trigonometric identities.

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


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:

`sqrt((1 - cosA)/(1 + cosA)) = cosec A - cot A`


Prove the following identities:

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


Prove that:

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


If x cos A + y sin A = m and x sin A – y cos A = n, then prove that : x2 + y2 = m2 + n2


`sin theta/((cot theta + cosec  theta)) - sin theta /( (cot theta - cosec  theta)) =2`


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


What is the value of 9cot2 θ − 9cosec2 θ? 


Prove the following identity : 

`sin^2Acos^2B - cos^2Asin^2B = sin^2A - sin^2B`


Given `cos38^circ sec(90^circ - 2A) = 1` , Find the value of <A


Prove that sin (90° - θ) cos (90° - θ) = tan θ. cos2θ.


If x = h + a cos θ, y = k + b sin θ. 
Prove that `((x - h)/a)^2 + ((y - k)/b)^2 = 1`.


Prove the following identities: sec2 θ + cosec2 θ = sec2 θ cosec2 θ.


Prove that: `1/(cosec"A" - cot"A") - 1/sin"A" = 1/sin"A" - 1/(cosec"A" + cot"A")`


Choose the correct alternative:

cot θ . tan θ = ?


Prove that `"cot A"/(1 - cot"A") + "tan A"/(1 - tan "A")` = – 1


If sin A = `1/2`, then the value of sec A is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×