Question

sin(45+x)+sin(45-x) equals to?​

Answer 1

Answer:

Step-by-step explanation:

sin (45+x) + sin(45-x)

(a+b) (a-b)

Answer 2

Step-by-step explanation:

Given:-

Sin (45+x) + Sin (45-x)

To find :-

Find the value of the expression ?

Solution :-

Given expression is Sin (45+x) + Sin (45-x)

We know that

Sin (A+B) = Sin A Cos B + Cos A Sin B

Sin (45+x) = Sin 45° Cos x + Cos 45° Sin x

=> Sin (45+x) = (1/√2)Cosx + (1/√2) Sin x

=> Sin (45+x) = (Cos x)/√2 + (Sin x)/√2

=> Sin (45+x) = (Cos x + Sin x)/√2

=> Sin (45+x) = (Sin x+ Cosx)/√2

and

Sin (A -B) = Sin A Cos B - Cos A Sin B

Sin (45-x) = Sin 45° Cos x - Cos 45° Sin x

=> Sin (45-x) = (1/√2)Cosx - (1/√2) Sin x

=> Sin (45-x) = (Cos x)/√2 - (Sin x)/√2

=> Sin (45-x) = (Cos x - Sin x)/√2

=> Sin (45-x) = (Sin x - Cosx)/√2

On applying this formula to the given expression then

=> Sin (45+x) + Sin (45-x)

=> (Sin x+ Cosx)/√2 + (Sin x - Cosx)/√2

=> [( (Sin x + Cosx)+ (Sin x - Cosx)]/√2

=> ( Sin x + Cos x + Sin x - Cos x)/√2

=> (Sin x + Sin x)/√2

=> (2 Sin x )/√2

=> (√2×√2× Sin x)/√2

=> √2 Sin x

Answer :-

The value of Sin (45+x)+Sin (45-x) = √2 Sin x

Used formulae:-

→ Sin (A+B) = Sin A Cos B + Cos A Sin B

→Sin (A -B) = Sin A Cos B - Cos A Sin B

→ Sin 45° = 1/√2

→ Cos 45° = 1/√2