Question

Let

α
and
β
be first quadrant angles with
cos
(
α
)
=
√
5
7
and
sin
(
β
)
=
√
5
3
.

Find
sin
(
α
−
β
)
.

Answer 1

2/7.

Explanation:

We know that:

• sin squared a + cos squared a = 1

So Sin a = √ (1 - cos^2 a).

Plugging in cos a = √5/7, we get a sin a = 2√5/7

Similarly we can find sin b = √5/3.

Now, we can use the angle subtraction formula to find sin(α−β):

sin(α−β)=sin α cos β−cos α sin β = 2√5/7 x √5/3 - √5/7 x √5/3 = 2/7.