If cos (α + β) = 0, then sin (α - β) can be reduced to
a. cos β
b. cos 2β
c. sin α
d. sin 2α

Solution:

Given, cos(α + β) = 0

We have to find the value of sin(α - β)

From the trigonometric ratios,

Given, cos(α + β) = 0

(α + β) = cos^-1(0)

Cos is zero at 90°

So, (α + β) = 90°

Now, α = 90° - β

Substitute the value of α,

sin(α - β) = sin (90° - β - β)

= sin(90° - 2β )

Using the trigonometric ratio of complementary angles,

 sin (90° - A) = cos A

So, sin (90° - 2β ) = cos 2β

Therefore, sin (α - β) = cos 2β

✦ Try This: If sin (α + β) = 1, then cos (α - β) can be reduced to

Given, sin(α + β) = 1

We have to find the value of cos(α - β)

From the trigonometric ratios of angles,

(α + β) = sin^-1(1)

(α + β) = 90°

So, α = 90° - β

Substituting the value of α,

Now, cos (α - β) = cos (90° - β - β)

= cos (90° - 2β)

Using the trigonometric ratio of complementary angles,

cos(90° - A) = sin A

So, cos (90° - 2β) = sin 2β

Therefore, cos (α - β) can be reduced to sin 2β.

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 8

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NCERT Exemplar Class 10 Maths Exercise 8.1 Problem 5

If cos (α + β) = 0, then sin (α - β) can be reduced to a. cos β, b. cos 2β, c. sin α, d. sin 2α

Summary:

If cos (α + β) = 0, then sin (α - β) can be reduced to cos 2β

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