Home » Maths formulas for class 9 10 11 12 » Sin 15 cos 15 degrees value

Sin 15 cos 15 degrees value

Sin 15 cos 15 degrees value

What is the value of Sin 15+Cos 15 degrees?

We have to use trigonometric identities to find the value of Sin 15 cos 15 degrees. We can find out the values of Sin 15+Cos 15 by using many other ways as well. Lets discuss in detail –

First we will explain how to find the value of sin 15 cos 15 degree. there is no formula to find the value of sin 15 degree but we have to use one of trigonometric identity (compound angle formula) Sin(A-B) = SinA cosB -CosA sinB. Now lets put A = 60 and B = 45

So we can say that Sin 15° = Sin(60°-45°). By using compound angle formula Sin(A-B) = SinA cosB -CosA sinB we can solve this. You can go through this link to find other formulas explanation and maths notes.

Value of Sin 15 degrees

First you have to rewrite Sin 15° as Sin (60°-45°) after that you have to apply compound angle formula Sin(A-B) = SinA cosB -CosA sinB

  • Sin 15° = Sin(60°-45°)
  • = Sin60cos45°-Cos60°sin45°
  • (√3/2)(1/√2) – (1/2)(1/√2)
  • = (√3 -1)/2√2
  • So Sin15° = (√3 -1)/2√2

Value of cos 15 degrees

First you have to rewrite Cos 15° as Cos (60°-45°) after that you have to apply compound angle formula Cos(A-B) = CosA cosB + SinA sinB

  • Cos 15° = Cos (60°-45°)
  • use Cos(A-B) = CosA cosB + SinA sinB formula
  • Cos60° cos45° + Sin60° sin45°
  • (1/2)(1/√2)+ (√3/2)(1/√2)
  • Cos 15° = 1/2√2 + √3/2√2
  • Cos 15° = (√3+1)/(2√2)

Find the value of sin15°+cos15°

We can rewrite sin(15) + cos(15) as sin(45 – 30) + cos(45- 30) after that we can apply compound angle formula Sin(A-B) = SinA cosB -CosA sinB and Cos(A-B) = CosA cosB + SinA sinB

  • sin(45 – 30) + cos(45- 30)
  • sin(45)cos(30) – cos(45)sin(30) + cos(45)cos(30) + sin(45)sin(30)
  • (1/√2)(√3/2) – (1/√2)(1/2) + (1/√2)(√3/2) + (1/√2)(1/2)
  • (2/√2)(√3/2)
  • √3/√2 (we can multiply numerator and denominator by √2)
  • √6/2

Trigonometry Formulas & Identities

  • sin θ = Opposite Side/Hypotenuse
  • cos θ = Adjacent Side/Hypotenuse
  • tan θ = Opposite Side/Adjacent Side
  • sec θ = Hypotenuse/Adjacent Side
  • cosec θ = Hypotenuse/Opposite Side
  • cot θ = Adjacent Side/Opposite Side
  • cosec θ = 1/sin θ
  • sec θ = 1/cos θ
  • cot θ = 1/tan θ
  • sin θ = 1/cosec θ
  • cos θ = 1/sec θ
  • tan θ = 1/cot θ

Trigonometry Table

Angles (In Degrees)30°45°60°90°180°270°360°
Angles (In Radians)π/6π/4π/3π/2π3π/2
sin01/21/√2√3/210-10
cos1√3/21/√21/20-101
tan01/√31√300
cot√311/√300
csc2√22/√31-1
sec12/√3√22-11

FAQs

How do you find the value of cos 15 and sin 15?

In this post we have explained the possible ways to find the values of sin15 and cos 15 degrees

What are the value of sin 15?

(√3 -1)/2√2

What is the value of 2 sin 15 degree cos 15 degree?

2 × sin 15° × cos 15° = sin 30°

Is the value of cos 15?

(√3+1)/(2√2)

How do you find sin 15?

(√3 -1)/2√2. Please follow this post

How do you find cos 15 without a calculator?

By using trigonometric identities. Please follow this post

Is sin 15 degrees rational?

yes. It is a rational number 

What is the value of cos 15 in fraction?

(√3+1)/(2√2)

Please Support us By Following our Social Media Channels
Telegram Channel —- Join Now !!
Facebook Page —- Join Now !!
Facebook Group —- Join Now !!
Share

Leave a Comment

Your email address will not be published. Required fields are marked *

error: Content is protected !!
Scroll to Top