Question

If A B one two complementary agus
then find the value of
sinA ×COSB + COSA× SinB​

Answer 1

Answer:

1

Step-by-step explanation:

Given,

A , B are complementary angles.

To Find :-

sinA × cosB + cosA × sinB

Formula Required :-

sin(A + B) = sinA × cosB + cosA × sinB

Sum of complementary angles = 90°

sin(90 - α) = cosα

cos(90 - α) = sinα

sin²α + cos²α = 1

How To Do :-

As they said that A,B are complementary angles we need to equate their sum to 90 and we need to subject either 'A' or 'B' then we need to substitute that value in 'sinA × cosB + cosA × sinB' and we need to simplify it then we need use a trigonometric identity and we need to find the value of it or we can directly use the formula of sin(A + B) and we can simplify it.

Solution :-

A , B are complementary angles.

→ A + B = 90°

→ A = 90° - B

Method 1 :-

sinA × cosB + cosA × sinB

Substituting the value of 'A' :-

= sin(90° - B) × cosB + cos(90° - B) × sinB

= cosB × cosB + sinB × sinB

[ ∴ sin(90 - α) = cosα

cos(90 - α) = sinα]

= cos²B + sin²B

= 1

[ ∴  sin²α + cos²α = 1]

Method 2 :-

sinA × cosB + cosA × sinB

= sin(A + B)

Substituting the Value of 'A' :-

= sin(90° - B + B)

= sin(90°)

= sin90°

= 1