हिंदी

If 4 tanθ = 3, then (4sinθ-cosθ4sinθ+cosθ) is equal to ______.

Advertisements
Advertisements

प्रश्न

If 4 tanθ = 3, then `((4 sintheta - costheta)/(4sintheta + costheta))` is equal to ______.

विकल्प

  • `2/3`

  • `1/3`

  • `1/2`

  • `3/4`

MCQ
रिक्त स्थान भरें
Advertisements

उत्तर

If 4 tanθ = 3, then `((4 sintheta - costheta)/(4sintheta + costheta))` is equal to `underlinebb(1/2)`.

Explanation:

Given,

4 tanθ = 3

⇒ tanθ = `3/4`   ...(i)

∴ `(4 sin theta - cos theta)/(4 sin theta + cos theta) = (4 sin theta/cos theta - 1)/(4 sin theta/cos theta + 1)`   ...[Divide by cos θ in both numerator and denominator]

= `(4 tan theta - 1)/(4 tan theta + 1)`  ...`[∵ tan theta = sin theta/cos theta]`

= `(4(3/4) - 1)/(4(3/4) + 1)`  ...[Put the value from equation (i)]

= `(3 - 1)/(3 + 1)`

= `2/4`

= `1/2`

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 8: Introduction To Trigonometry and Its Applications - Exercise 8.1 [पृष्ठ ९१]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 10
अध्याय 8 Introduction To Trigonometry and Its Applications
Exercise 8.1 | Q 12 | पृष्ठ ९१

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

If cot θ = `7/8`, evaluate cot2 θ.


In ΔABC, right angled at B. If tan A = `1/sqrt3` , find the value of

  1.  sin A cos C + cos A sin C
  2. cos A cos C − sin A sin C

In ΔPQR, right angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P.


State whether the following are true or false. Justify your answer.

cos A is the abbreviation used for the cosecant of angle A.


State whether the following are true or false. Justify your answer.

sin θ = `4/3`, for some angle θ.


If 4 tan θ = 3, evaluate `((4sin theta - cos theta + 1)/(4sin theta + cos theta - 1))`


In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.

`cos theta = 7/25`


In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.

`tan theta = 8/15`


In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.

`cosec theta = sqrt10`


if `tan theta = 12/13` Find `(2 sin theta cos theta)/(cos^2 theta - sin^2 theta)`


Evaluate the following:

(cosec2 45° sec2 30°)(sin2 30° + 4 cot2 45° − sec2 60°)


Find the value of x in the following :

cos 2x = cos 60° cos 30° + sin 60° sin 30°


If cos A + cos² A = 1, then sin² A + sin4 A is equal to ______.


5 tan² A – 5 sec² A + 1 is equal to ______.


Prove the following:

If tan A = `3/4`, then sinA cosA = `12/25`


Find will be the value of cos 90° + sin 90°.


Let tan9° = `(1 - sqrt((sqrt(5)k)/m))k` where k = `sqrt(5) + 1` then m is equal to  ______.


If sinθ = `1/sqrt(2)` and `π/2 < θ < π`. Then the value of `(sinθ + cosθ)/tanθ` is ______.


(3 sin2 30° – 4 cos2 60°) is equal to ______.


Evaluate: 5 cosec2 45° – 3 sin2 90° + 5 cos 0°.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×