English
Tamil Nadu Board of Secondary EducationHSC Science Class 11

Prove that cos(π + θ) = − cos θ - Mathematics

Advertisements
Advertisements

Question

Prove that cos(π + θ) = − cos θ

Sum

Solution

L..H.S = cos(π + θ)

= cos(180° + θ)

= cos 180° cos θ – sin 180° sin θ

= (– 1) cos θ – (0) sin θ

= – cos 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. (ii) | Page 109

RELATED QUESTIONS

Find the values of sin (– 1110°)


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


Find the value of the trigonometric functions for the following:
tan θ = −2, θ lies in the II 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 x = `15/17` and cos y = `12/13, 0 < x < pi/2, 0 < y < pi/2`, find the value of cos(x − y)


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


Prove that sin 75° – sin 15° = cos 105° + cos 15°


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


Show that tan(45° − A) = `(1 - tan "A")/(1 + tan "A")`


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


Find the value of cos 2A, A lies in the first quadrant, when tan A  `16/63`


If cos θ = `1/2 ("a" + 1/"a")`, show that cos 3θ = `1/2 ("a"^3 + 1/"a"^3)`


Prove that (1 + tan 1°)(1 + tan 2°)(1 + tan 3°) ..... (1 + tan 44°) is a multiple of 4


Express the following as a sum or difference
sin 4x cos 2x


Express the following as a sum or difference
cos 5θ  cos 2θ


Show that `cos  pi/15  cos  (2pi)/15  cos  (3pi)/15  cos  (4pi)/15  cos  (5pi)/15  cos  (6pi)/15  cos  (7pi)/15 = 1/128`


Show that `((cos theta -cos 3theta)(sin 8theta + sin 2theta))/((sin 5theta - sin theta) (cos 4theta - cos 6theta))` = 1


If x + y + z = xyz, then prove that `(2x)/(1 - x^2) + (2y)/(1 - y^2) + (2z)/(1 - z^2) = (2x)/(1 - x^2) (2y)/(1 - y^2) (2z)/(1 - z^2)`


If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that sinB + sinC = 1


If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that cos B – cos C = `- 1 + 2sqrt(2) cos  "B"/2  sin  "C"/2`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×