मराठी

What is the Value of (1 − Cos2 θ) Cosec2 θ? - Mathematics

Advertisements
Advertisements

प्रश्न

What is the value of (1 − cos2 θ) cosec2 θ? 

थोडक्यात उत्तर

उत्तर

We have, 

`(1-cos^2 θ) cosec ^2 θ=sin^2θ xx cosec^2 θ`

=` sin^2θ xx(1/sin θ)^2` 

= `sin^2 θ xx1/( sin^2θ)` 

`= 1`

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 11: Trigonometric Identities - Exercise 11.3 [पृष्ठ ५५]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 10
पाठ 11 Trigonometric Identities
Exercise 11.3 | Q 2 | पृष्ठ ५५

संबंधित प्रश्‍न

 

Evaluate

`(sin ^2 63^@ + sin^2 27^@)/(cos^2 17^@+cos^2 73^@)`

 

As observed from the top of an 80 m tall lighthouse, the angles of depression of two ships on the same side of the lighthouse of the horizontal line with its base are 30° and 40° respectively. Find the distance between the two ships. Give your answer correct to the nearest meter.


Prove the following trigonometric identities.

`(cos theta)/(cosec theta + 1) + (cos theta)/(cosec theta - 1) = 2 tan theta`


Prove the following trigonometric identities

If x = a sec θ + b tan θ and y = a tan θ + b sec θ, prove that x2 − y2 = a2 − b2


If sin A + cos A = m and sec A + cosec A = n, show that : n (m2 – 1) = 2 m


Prove that:

`(sinA - cosA)(1 + tanA + cotA) = secA/(cosec^2A) - (cosecA)/(sec^2A)`


If a cos `theta + b sin theta = m and a sin theta - b cos theta = n , "prove that "( m^2 + n^2 ) = ( a^2 + b^2 )`


sec4 A − sec2 A is equal to


(sec A + tan A) (1 − sin A) = ______.


Prove the following identity :

`cos^4A - sin^4A = 2cos^2A - 1`


Prove the following identity : 

`sqrt((secq - 1)/(secq + 1)) + sqrt((secq + 1)/(secq - 1))` = 2 cosesq


Without using trigonometric identity , show that :

`sin(50^circ + θ) - cos(40^circ - θ) = 0`


Prove that sin2 θ + cos4 θ = cos2 θ + sin4 θ.


Prove that `( tan A + sec A - 1)/(tan A - sec A + 1) = (1 + sin A)/cos A`.


Prove that `((tan 20°)/(cosec 70°))^2 + ((cot 20°)/(sec 70°))^2  = 1`


Prove that: `(1 + cot^2 θ/(1 + cosec θ)) = cosec θ`.


If sec θ + tan θ = `sqrt(3)`, complete the activity to find the value of sec θ – tan θ

Activity:

`square` = 1 + tan2θ    ......[Fundamental trigonometric identity]

`square` – tan2θ = 1

(sec θ + tan θ) . (sec θ – tan θ) = `square`

`sqrt(3)*(sectheta - tan theta)` = 1

(sec θ – tan θ) = `square`


If cos θ = `24/25`, then sin θ = ?


Prove that sec2θ − cos2θ = tan2θ + sin2θ


Prove that (1 – cos2A) . sec2B + tan2B(1 – sin2A) = sin2A + tan2B


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×