English
Tamil Nadu Board of Secondary EducationHSC Science Class 11

Prove that sin(π + θ) = − sin θ. - Mathematics

Advertisements
Advertisements

Question

Prove that sin(π + θ) = − sin θ.

Sum

Solution

L.H.S = sin(π + θ)

= sin π cos θ + cos π sin θ

= (0) cos θ + (– 1) sin θ

= – sin θ

= R.H.S

shaalaa.com
Trigonometric Functions and Their Properties
  Is there an error in this question or solution?
Chapter 3: Trigonometry - Exercise 3.4 [Page 109]

APPEARS IN

Samacheer Kalvi Mathematics - Volume 1 and 2 [English] Class 11 TN Board
Chapter 3 Trigonometry
Exercise 3.4 | Q 6. (iii) | Page 109

RELATED QUESTIONS

Find the values of tan(1050°)


Find the values of `sin (-(11pi)/3)`


`(5/7, (2sqrt(6))/7)` is a point on the terminal side of an angle θ in standard position. Determine the six trigonometric function values of angle θ


Find the value of the trigonometric functions for the following:
cos θ = `2/3`, θ lies in the I quadrant


Find the value of the trigonometric functions for the following:
sec θ = `13/5`, θ lies in the IV quadrant


If sin x = `15/17` and cos y = `12/13, 0 < x < pi/2, 0 < y < pi/2` find the value of sin(x + y)


If sin A = `3/5` and cos B = `9/41 0 < "A" < pi/2, 0 < "B" < pi/2`, find the value of sin(A + B)


Prove that sin(45° + θ) – sin(45° – θ) = `sqrt(2) sin θ`


Prove that cos(A + B) cos C – cos(B + C) cos A = sin B sin(C – A)


Prove that cos(A + B) cos(A – B) = cos2A – sin2B = cos2B – sin2A


Prove that `tan(pi/4 + theta) tan((3pi)/4 + theta)` = – 1


If θ + Φ = α and tan θ = k tan Φ, then prove that sin(θ – Φ) = `("k" - 1)/("k" + 1)` sin α


If A + B = 45°, show that (1 + tan A)(1 + tan B) = 2


Prove that `(sin 4x + sin 2x)/(cos 4x + cos 2x)` = tan 3x


Prove that cos(30° – A) cos(30° + A) + cos(45° – A) cos(45° + A) = `cos 2"A" + 1/4`


If A + B + C = 180◦, prove that sin 2A + sin 2B + sin 2C = 4 sin A sin B sin C


If A + B + C = 180°, prove that sin(B + C − A) + sin(C + A − B) + sin(A + B − C) = 4 sin A sin B sin C


Choose the correct alternative:
If cos 28° + sin 28° = k3, then cos 17° is equal to


Choose the correct alternative:
Let fk(x) = `1/"k" [sin^"k" x + cos^"k" x]` where x ∈ R and k ≥ 1. Then f4(x) − f6(x) = 


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×