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)	0°	30°	45°	60°	90°	180°	270°	360°
Angles (In Radians)	0°	π/6	π/4	π/3	π/2	π	3π/2	2π
sin	0	1/2	1/√2	√3/2	1	0	-1	0
cos	1	√3/2	1/√2	1/2	0	-1	0	1
tan	0	1/√3	1	√3	∞	0	∞	0
cot	∞	√3	1	1/√3	0	∞	0	∞
csc	∞	2	√2	2/√3	1	∞	-1	∞
sec	1	2/√3	√2	2	∞	-1	∞	1

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