मराठी

Write the Value of `(1 - Cos^2 Theta ) Cosec^2 Theta`.

Advertisements
Advertisements

प्रश्न

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

Advertisements

उत्तर

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

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

    =1

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 13: Trigonometric identities - Exercises 3

APPEARS IN

आर. एस. अग्रवाल Mathematics [English] Class 10
पाठ 13 Trigonometric identities
Exercises 3 | Q 2

संबंधित प्रश्‍न

The angles of depression of two ships A and B as observed from the top of a light house 60 m high are 60° and 45° respectively. If the two ships are on the opposite sides of the light house, find the distance between the two ships. Give your answer correct to the nearest whole number.


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 the following identities:

(1 – tan A)2 + (1 + tan A)2 = 2 sec2A


Prove the following identities:

`tan^2A - tan^2B = (sin^2A - sin^2B)/(cos^2A * cos^2B)`


Prove the following identities:

`1 - cos^2A/(1 + sinA) = sinA`


Prove the following identities:

`cosA/(1 + sinA) + tanA = secA`


Prove the following identities:

`(1 - 2sin^2A)^2/(cos^4A - sin^4A) = 2cos^2A - 1`


If `( cosec theta + cot theta ) =m and ( cosec theta - cot theta ) = n, ` show that mn = 1.


Write the value of `sin theta cos ( 90° - theta )+ cos theta sin ( 90° - theta )`. 


If sec2 θ (1 + sin θ) (1 − sin θ) = k, then find the value of k.


If x = a sec θ and y = b tan θ, then b2x2 − a2y2 =


If a cos θ − b sin θ = c, then a sin θ + b cos θ =


Prove the following identity : 

`(secθ - tanθ)^2 = (1 - sinθ)/(1 + sinθ)`


Prove the following identity : 

`(tanθ + 1/cosθ)^2 + (tanθ - 1/cosθ)^2 = 2((1 + sin^2θ)/(1 - sin^2θ))`


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


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


Prove the following identities:
`1/(sin θ + cos θ) + 1/(sin θ - cos θ) = (2sin θ)/(1 - 2 cos^2 θ)`.


If `tan θ = 9/40`, complete the activity to find the value of sec θ.

Activity:

sec2θ = 1 + `square`   ...[Fundamental trigonometric identity]

sec2θ = 1 + `square^2`

sec2θ = 1 + `square` 

sec θ = `square` 


Show that `(cos^2(45^circ + θ) + cos^2(45^circ - θ))/(tan(60^circ + θ) tan(30^circ - θ)) = 1`


tan θ × `sqrt(1 - sin^2 θ)` is equal to:


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×