Question

If sin θ = `12/13, (0 < θ < π/2)` and cos `phi = - 3/5, (π < phi < (3π)/2)`. Then, sin(θ + `phi`) will be ______.

Options

• `(-56)/61`

• `(-56)/65`

• `1/65`

• – 56

Answer 1

If sin θ = `12/13, (0 < θ < π/2)` and cos `phi = - 3/5, (π < phi < (3π)/2)`. Then, sin(θ + `phi`) will be `underlinebb((-56)/65)`.

Explanation:

We have, sin θ = `12/13`

cos θ = `sqrt(1 - sin^2θ)`

= `sqrt(1 - (12/13)^2`

= `5/13`

and cos `phi = (-3)/5`

sin `phi = sqrt(1 - 9/25)`

= `(-4)/5`  ...`[∵ π < phi < (3π)/2]`

Now, sin(θ + `phi`) = sin θ . cos `phi` + cos θ . sin `phi`

= `(12/13)((-3)/5) + (5/13)((-4)/5)`

= `(-36)/65 - 20/65`

= `(-56)/65`