Question

Express as sum or difference of trigonometrical ratios—
(i) 2sin5∅ sin7∅
(ii) sin80° sin40°​

Answer 1

Answer:

We will how to express the sum or difference as a product.

We will how to express the sum or difference as a product.1. Convert sin 7α + sin 5α as a product.

We will how to express the sum or difference as a product.1. Convert sin 7α + sin 5α as a product.Solution:

We will how to express the sum or difference as a product.1. Convert sin 7α + sin 5α as a product.Solution:sin 7α + sin 5α

We will how to express the sum or difference as a product.1. Convert sin 7α + sin 5α as a product.Solution:sin 7α + sin 5α= 2 sin (7α + 5α)/2 cos (7α - 5α)/2, [Since, sin α + sin β = 2 sin (α + β)/2 cos (α - β)/2]

We will how to express the sum or difference as a product.1. Convert sin 7α + sin 5α as a product.Solution:sin 7α + sin 5α= 2 sin (7α + 5α)/2 cos (7α - 5α)/2, [Since, sin α + sin β = 2 sin (α + β)/2 cos (α - β)/2]= 2 sin 6α cos α

We will how to express the sum or difference as a product.1. Convert sin 7α + sin 5α as a product.Solution:sin 7α + sin 5α= 2 sin (7α + 5α)/2 cos (7α - 5α)/2, [Since, sin α + sin β = 2 sin (α + β)/2 cos (α - β)/2]= 2 sin 6α cos α2. Express sin 7A + sin 4A as a product.

We will how to express the sum or difference as a product.1. Convert sin 7α + sin 5α as a product.Solution:sin 7α + sin 5α= 2 sin (7α + 5α)/2 cos (7α - 5α)/2, [Since, sin α + sin β = 2 sin (α + β)/2 cos (α - β)/2]= 2 sin 6α cos α2. Express sin 7A + sin 4A as a product.Solution:

We will how to express the sum or difference as a product.1. Convert sin 7α + sin 5α as a product.Solution:sin 7α + sin 5α= 2 sin (7α + 5α)/2 cos (7α - 5α)/2, [Since, sin α + sin β = 2 sin (α + β)/2 cos (α - β)/2]= 2 sin 6α cos α2. Express sin 7A + sin 4A as a product.Solution:sin 7A + sin 4A

We will how to express the sum or difference as a product.1. Convert sin 7α + sin 5α as a product.Solution:sin 7α + sin 5α= 2 sin (7α + 5α)/2 cos (7α - 5α)/2, [Since, sin α + sin β = 2 sin (α + β)/2 cos (α - β)/2]= 2 sin 6α cos α2. Express sin 7A + sin 4A as a product.Solution:sin 7A + sin 4A= 2 sin (7A + 4A)/2 cos (7A - 4A)/2

We will how to express the sum or difference as a product.1. Convert sin 7α + sin 5α as a product.Solution:sin 7α + sin 5α= 2 sin (7α + 5α)/2 cos (7α - 5α)/2, [Since, sin α + sin β = 2 sin (α + β)/2 cos (α - β)/2]= 2 sin 6α cos α2. Express sin 7A + sin 4A as a product.Solution:sin 7A + sin 4A= 2 sin (7A + 4A)/2 cos (7A - 4A)/2= 2 sin (11A/2) cos (3A)/2

Answer 2

Step-by-step explanation:

sinA+sinB=2sin( A+B/2)cos( A−B/2)

=2sin( 5θ+7θ/2)cos(5θ−7θ/2)

=2sin6θcos1θ

sin 80 + sin 40

= 2 sin (80+ 40)/2 cos (80 - 40)/2

= 2 sin (12/2) cos (4)/2

=2sin6cos2