If 𝑐𝑜𝑠 (α + β) = 0, then 𝑠𝑖𝑛 (α − β) can be reduced to

# If 𝑐𝑜𝑠 (α + β) = 0, then 𝑠𝑖𝑛 (α − β) can be reduced to

1. A

𝑐𝑜𝑠 β

2. B

𝑐𝑜𝑠 2β

3. C

𝑠𝑖𝑛 α

4. D

𝑠𝑖𝑛 2α

Fill Out the Form for Expert Academic Guidance!l

+91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)

### Solution:

We have been given that 𝑐𝑜𝑠 (α + β) = 0

We know that 𝑐𝑜𝑠 90° = 0

⇒ 𝑐𝑜𝑠 (α + β) = 𝑐𝑜𝑠 90°

⇒ α + β = 90°

⇒ α = 90° − β

Substituting the value of α from the above equation, we get

Now, 𝑠𝑖𝑛 (α − β) = 𝑠𝑖𝑛 (90° − β − β)

⇒ 𝑠𝑖𝑛 (α − β) = 𝑠𝑖𝑛 (90° − 2β)

We know that, for any angle θ, 𝑠𝑖𝑛 (90° − θ) = 𝑐𝑜𝑠 θ

Therefore we can say that, 𝑠𝑖𝑛 (90° − 2β) = 𝑐𝑜𝑠 2β

Hence, here 𝑠𝑖𝑛 (α − β) can be reduced to 𝑐𝑜𝑠 2β.

## Related content

 Area of Square Area of Isosceles Triangle Pythagoras Theorem Triangle Formulae Perimeter of Triangle Formula Area Formulae Volume of Cone Formula Matrices and Determinants_mathematics Critical Points Solved Examples Type of relations_mathematics  +91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)