Question

writing sum of multiples of sin and cos as single sin functons

Answer 1

The answer is given below :

The question asks to write down sum of multiples of sine and cosine as single sine function.

There is a formula :

sinα cosβ + cosα sinβ

= sin (α + β),
which is the required sine function.

Example :

Let, α = 45° and β = 45°

Now, we use the formula

sin (α + β) = sinα cosβ + cosα sinβ.

We put α = π/4 and β = π/4

L.H.S. = sin (α + β)

= sin (π/4 + π/4)

= sin (π/2)

= 1

R.H.S. = sinα cosβ + cosα sinβ

= sin (π/4) cos (π/4) + cos (π/4) sin (π/4)

= (1/√2 × 1/√2) + (1/√2 × 1/√2)

= 1/2 + 1/2

= 1

So, the formula is confirmed.

Thank you for your question.