मराठी

Write the Value of ` Sin^2 Theta Cos^2 Theta (1+ Tan^2 Theta ) (1+ Cot^2 Theta).` - Mathematics

Advertisements
Advertisements

प्रश्न

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

उत्तर

`sin^2 theta cos^2 theta (1+ tan^2 theta ) (1+ cot^2 theta)`

     =`sin^2 theta cos^2 theta sec^2 theta cosec^2 theta `

     = ` sin^2 theta xx cos^2 xx 1/cos^2 theta xx1/sin^2 theta`

     = 1

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 8: Trigonometric Identities - Exercises 3

APPEARS IN

आर एस अग्रवाल Mathematics [English] Class 10
पाठ 8 Trigonometric Identities
Exercises 3 | Q 11

संबंधित प्रश्‍न

`"If "\frac{\cos \alpha }{\cos \beta }=m\text{ and }\frac{\cos \alpha }{\sin \beta }=n " show that " (m^2 + n^2 ) cos^2 β = n^2`

 


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 cos^3 theta, y = b sin^3 theta` " prove that " `(x/a)^(2/3) + (y/b)^(2/3) = 1`


Prove the following identities:

`cosA/(1 - sinA) = sec A + tan A`


Prove the following identities:

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


Prove the following identities:

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


Prove the following identities:

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


Prove that:

(tan A + cot A) (cosec A – sin A) (sec A – cos A) = 1


`{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)`


`(tan A + tanB )/(cot A + cot B) = tan A tan B`


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


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


Prove the following identity :

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


Prove the following identity :

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


Prove the following identity : 

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


Prove the following identity : 

`2(sin^6θ + cos^6θ) - 3(sin^4θ + cos^4θ) + 1 = 0`


Prove that cos θ sin (90° - θ) + sin θ cos (90° - θ) = 1.


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


Prove that `(1 + sintheta)/(1 - sin theta)` = (sec θ + tan θ)2 


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×