मराठी

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

Advertisements
Advertisements

प्रश्न

Write the value of `(1+ tan^2 theta ) ( 1+ sin theta ) ( 1- sin theta)`

उत्तर

`(1+ tan^2 theta )(1+ sin theta )(1- sintheta)`

    =` sec^2 theta (1- sin^2 theta )`

    =`1/ cos^2 theta xx cos^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 12

संबंधित प्रश्‍न

Prove the following trigonometric identities.

sin2 A cot2 A + cos2 A tan2 A = 1


Prove the following trigonometric identities.

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


Prove the following trigonometric identity.

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


Prove the following identities:

`secA/(secA + 1) + secA/(secA - 1) = 2cosec^2A`


Prove the following identities:

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


If m = a sec A + b tan A and n = a tan A + b sec A, then prove that : m2 – n2 = a2 – b2


Prove the following identities:

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


If x = a cos θ and y = b cot θ, show that:

`a^2/x^2 - b^2/y^2 = 1` 


`costheta/((1-tan theta))+sin^2theta/((cos theta-sintheta))=(cos theta+ sin theta)`


If `cos B = 3/5 and (A + B) =- 90° ,`find the value of sin A.


Prove the following identity :

`tan^2A - sin^2A = tan^2A.sin^2A`


Prove the following identity :

(secA - cosA)(secA + cosA) = `sin^2A + tan^2A`


Prove the following identity :

`sec^2A.cosec^2A = tan^2A + cot^2A + 2`


Prove the following identity :

`tanA - cotA = (1 - 2cos^2A)/(sinAcosA)`


Prove that:

tan (55° + x) = cot (35° – x)


Prove that: `(sin θ - 2sin^3 θ)/(2 cos^3 θ - cos θ) = tan θ`.


If a cos θ – b sin θ = c, then prove that (a sin θ + b cos θ) = `±  sqrt("a"^2 + "b"^2 -"c"^2)`


If sin θ + sin2 θ = 1 show that: cos2 θ + cos4 θ = 1


Prove that `(sintheta + tantheta)/cos theta` = tan θ(1 + sec θ)


Let α, β be such that π < α – β < 3π. If sin α + sin β = `-21/65` and cos α + cos β = `-27/65`, then the value of `cos  (α - β)/2` is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×