Question

if sin (A-B)=1/2,cos (A+B)=1/2, then find A and B​

Answer 1

$\textbf{\large{\underline{\pink{ Answer: }}}}$

Sin(A-B)=1/2

we know that Sin 30° =1/2

So ,

Sin(A-B) = Sin30°

(A-B) =30 °--------(eq 1)

And aslo,

Cos(A+B)= 1/2

Cos60°=1/2

Cos(A+B) =Cos 60°

(A+B) = 60°--------(eq 2)

Adding equation 1 and 2

A-B+A+B= 30+60

-B and +B are cancelled So, we get

2A=90

Then, A= 45

So Substitute A value in equation -2

A+B= 60

45+B=60

B= 60-45

B= 15

Value of A and B are 45 and 15

More Information:

Trigon metric Identities

sin²θ + cos²θ = 1

sec²θ - tan²θ = 1

csc²θ - cot²θ = 1

Trigometric relations

sinθ = 1/cscθ

cosθ = 1 /secθ

tanθ = 1/cotθ

tanθ = sinθ/cosθ

cotθ = cosθ/sinθ

Trigonmetric ratios

sinθ = opp/hyp

cosθ = adj/hyp

tanθ = opp/adj

cotθ = adj/opp

cscθ = hyp/opp

secθ = hyp/adj