हिंदी

`Cos^2 Theta + 1/((1+ Cot^2 Theta )) =1` - Mathematics

Advertisements
Advertisements

प्रश्न

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

     

उत्तर

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

      =` cos^2 theta + 1/(cosec^2  theta)`

      =` cos^2  theta + sin^2 theta`

      =1

      =RHS

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 8: Trigonometric Identities - Exercises 1

APPEARS IN

आरएस अग्रवाल Mathematics [English] Class 10
अध्याय 8 Trigonometric Identities
Exercises 1 | Q 5.3

संबंधित प्रश्न

Prove the following identities, where the angles involved are acute angles for which the expressions are defined.

`(sintheta - 2sin^3theta)/(2costheta - costheta) =tan theta`

 


Evaluate without using trigonometric tables:

`cos^2 26^@ + cos 64^@ sin 26^@ + (tan 36^@)/(cot 54^@)`


Prove the following trigonometric identities.

if `T_n = sin^n theta + cos^n theta`, prove that `(T_3 - T_5)/T_1 = (T_5 - T_7)/T_3`


Prove the following identities:

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


Prove that:

2 sin2 A + cos4 A = 1 + sin4


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


Write the value of `(1 - cos^2 theta ) cosec^2 theta`.


If `cos theta = 2/3 , " write the value of" (4+4 tan^2 theta).`


If `sec theta = x ,"write the value of tan"  theta`.


Four alternative answers for the following question are given. Choose the correct alternative and write its alphabet:

sin θ × cosec θ = ______


If \[\sin \theta = \frac{4}{5}\] what is the value of cotθ + cosecθ? 


If \[\cos A = \frac{7}{25}\]  find the value of tan A + cot A. 


If cosec2 θ (1 + cos θ) (1 − cos θ) = λ, then find the value of λ. 


If sec θ + tan θ = x, then sec θ =


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


Prove the following identity :

cosecθ(1 + cosθ)(cosecθ - cotθ) = 1


If tanA + sinA = m and tanA - sinA = n , prove that (`m^2 - n^2)^2` = 16mn 


Without using a trigonometric table, prove that
`(cos 70°)/(sin 20°) + (cos 59°)/(sin 31°) - 8sin^2 30° = 0`.


Prove that sec2θ + cosec2θ = sec2θ × cosec2θ


Which of the following is true for all values of θ (0° ≤ θ ≤ 90°)?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×