English
Tamil Nadu Board of Secondary EducationHSC Science Class 11

Find the value of cos 105°.

Advertisements
Advertisements

Question

Find the value of cos 105°.

Sum
Advertisements

Solution

cos 105° = cos(60° + 45°)

= [cos 60° cos 45° – sin 60° sin 45°]

= `[1/2*1/sqrt2-sqrt(3)/2*1/sqrt(2)]`

= `(1-sqrt3)/(2sqrt2)`

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 5. (i) | Page 109

RELATED QUESTIONS

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


Find the value of the trigonometric functions for the following:
cos θ = `2/3`, θ lies in the I 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 cos(A – B)


Find the value of tan `(7pi)/12`


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


Prove that sin2(A + B) – sin2(A – B) = sin2A sin2B


Find the value of tan(α + β), given that cot α = `1/2`, α ∈ `(pi, (3pi)/2)` and sec β = `- 5/3` β ∈ `(pi/2, pi)`


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


Prove that cos 5θ = 16 cos5θ – 20 cos3θ + 5 cos θ


Prove that `tan (pi/4 + theta) - tan(pi/4 - theta)` = 2 tan 2θ


Prove that `32(sqrt(3)) sin  pi/48  cos  pi/48  cos  pi/24  cos  pi/12  cos  pi/6` = 3


Express the following as a sum or difference
2 sin 10θ  cos 2θ


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


Show that sin 12° sin 48° sin 54° = `1/8`


Prove that `(sin x + sin 3x + sin 5x + sin 7x)/(cos x + cos x + cos 5x  cos 7x)` = tan 4x


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


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 cos2 B + cos2 C = 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×