Question

If sinB = cos(2b-30) where 2B is a acute angle find the value of B.

plz answer​

Answer 1

Answer:

see the answer in explanation

Step-by-step explanation:

Sin b = cos(2b-30) given-1

we know that

sinb=cos(90-b) by property -2

equating 1 and 2

cos(2b-30)=cos(90-b)

therefore

2b-30=90-b

3b=120

b=120/3=40

also 2b is given to be acute angle will be 80

Answer 2

Answer- The above question is from the chapter 'Introduction to Trigonometry'.

Trigonometry- The branch of Mathematics which helps in dealing with measure of three sides of a right-angled triangle is called Trigonometry.

Trigonometric Ratios:

sin θ  = Perpendicular/Hypotenuse

cos θ = Base/Hypotenuse

tan θ = Perpendicular/Base

cosec θ = Hypotenuse/Perpendicular

sec θ = Hypotenuse/Base

cot θ = Base/Perpendicular

Also, tan θ = sin θ/cos θ and cot θ = cos θ/sinθ.

Trigonometric Identites:

1. sin²θ + cos²θ = 1

2. sec²θ - tan²θ = 1

3. cosec²θ - cot²θ = 1

T-Ratios of Complementary Angles:

1. sin(90°-θ)= cos θ

2. cos(90°- θ)= sin θ

3. tan(90°- θ)= cot θ

4. cosec(90°- θ)= sec θ

5. sec(90°- θ)= cosec θ

6. cot(90°- θ)= tan θ

Given question: If sin B = cos (2B - 30°) where 2B is a acute angle, find the value of B.

Solution: We know that cos(90°- θ)= sin θ.

⇒ sin B = cos (90° - B)

It is given that, sin B = cos (2B - 30°)

cos (90° - B) = cos (2B - 30°)

⇒ 90° - B = 2B - 30° (∵T-Ratios will get cancelled.)

⇒ 3B = 120°

⇒ B = 40°

∴ The value of B = 40°.