मराठी

If 2sin2θ – cos2θ = 2, then find the value of θ.

Advertisements
Advertisements

प्रश्न

If 2sin2θ – cos2θ = 2, then find the value of θ.

बेरीज
Advertisements

उत्तर

Given,

2sin2θ – cos2θ = 2

⇒ 2sin2θ – (1 – sin2θ) = 2  ...[∵ sin2θ + cos2θ = 1]

⇒ 2sin2θ + sin2θ – 1 = 2

⇒ 3sin2θ = 3

⇒ sin2θ = 1

⇒ sinθ = 1 = sin 90°  ...[∵ sin 90° = 1]

∴ θ = 90°

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 8: Introduction To Trigonometry and Its Applications - Exercise 8.3 [पृष्ठ ९५]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 10
पाठ 8 Introduction To Trigonometry and Its Applications
Exercise 8.3 | Q 12 | पृष्ठ ९५

संबंधित प्रश्‍न

if `cos theta = 5/13` where `theta` is an acute angle. Find the value of `sin theta`


Prove the following trigonometric identities.

`sqrt((1 - cos theta)/(1 + cos theta)) = cosec theta - cot theta`


Prove the following trigonometric identities.

sec A (1 − sin A) (sec A + tan A) = 1


Prove the following trigonometric identities.

sin2 A cot2 A + cos2 A tan2 A = 1


Prove the following trigonometric identities. `(1 - cos A)/(1 + cos A) = (cot A - cosec A)^2`


Prove the following identities:

(sec A – cos A) (sec A + cos A) = sin2 A + tan2


Prove the following identities:

`(cosecA - 1)/(cosecA + 1) = (cosA/(1 + sinA))^2`


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


`(tan theta)/((sec theta -1))+(tan theta)/((sec theta +1)) = 2 sec theta`


`sqrt((1-cos theta)/(1+cos theta)) = (cosec  theta - cot  theta)`


Write the value of ` sec^2 theta ( 1+ sintheta )(1- sintheta).`


Write the value of `4 tan^2 theta  - 4/ cos^2 theta`


Write the value of cosec2 (90° − θ) − tan2 θ. 


If x = asecθ + btanθ and y = atanθ + bsecθ , prove that `x^2 - y^2 = a^2 - b^2`


Given `cos38^circ sec(90^circ - 2A) = 1` , Find the value of <A


Without using trigonometric identity , show that :

`sec70^circ sin20^circ - cos20^circ cosec70^circ = 0`


Prove that (sin θ + cosec θ)2 + (cos θ + sec θ)2 = 7 + tanθ + cotθ. 


Prove that sin4A – cos4A = 1 – 2cos2A


Prove that (1 – cos2A) . sec2B + tan2B(1 – sin2A) = sin2A + tan2B


If 5 tan β = 4, then `(5  sin β - 2 cos β)/(5 sin β + 2 cos β)` = ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×