English

Write the Value of `(1 + Cot^2 Theta ) Sin^2 Theta`.

Advertisements
Advertisements

Question

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

Advertisements

Solution

  =`(1+ cot^2 theta ) sin ^2 theta`

  =` cosec ^2 theta xx 1/ ( cosec^2 theta)`

 =1

shaalaa.com
  Is there an error in this question or solution?
Chapter 13: Trigonometric identities - Exercises 3

APPEARS IN

R.S. Aggarwal Mathematics [English] Class 10
Chapter 13 Trigonometric identities
Exercises 3 | Q 4

RELATED QUESTIONS

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

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


Prove the following trigonometric identities.

(sec A + tan A − 1) (sec A − tan A + 1) = 2 tan A


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


Prove that:

`(cos^3A + sin^3A)/(cosA + sinA) + (cos^3A - sin^3A)/(cosA - sinA) = 2`


Prove the following identities:

(1 + tan A + sec A) (1 + cot A – cosec A) = 2


`(1+ cos theta)(1- costheta )(1+cos^2 theta)=1`


If `tan theta = 1/sqrt(5), "write the value of" (( cosec^2 theta - sec^2 theta))/(( cosec^2 theta - sec^2 theta))`.


Prove that:

`"tanθ"/("secθ"  –  1) = (tanθ + secθ + 1)/(tanθ + secθ - 1)`


If x = a sec θ cos ϕ, y = b sec θ sin ϕ and z = c tan θ, then\[\frac{x^2}{a^2} + \frac{y^2}{b^2}\]


If  cos (\[\alpha + \beta\]= 0 , then sin \[\left( \alpha - \beta \right)\] can be reduced to  

 


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


Without using trigonometric identity , show that :

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


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


Prove that: sin4 θ + cos4θ = 1 - 2sin2θ cos2 θ.


Prove that identity:
`(sec A - 1)/(sec A + 1) = (1 - cos A)/(1 + cos A)`


Prove that `"cosec"  θ xx sqrt(1 - cos^2θ) = 1`.


Prove that `sqrt((1 + cos A)/(1 - cos A)) = "cosec"  A + cot A`.


If tan α + cot α = 2, then tan20α + cot20α = ______.


The value of tan A + sin A = M and tan A - sin A = N.

The value of `("M"^2 - "N"^2) /("MN")^0.5`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×