Question

If cos (A + B) = 0 and cot (A –B) =
$\sqrt{3}$
find the value of A and B.​

Answer 1

What would you like to ask?

MATHS

avatar

Asked on December 26, 2019 by

Hazel Khanande

If sin(A+B)=1 and cos(A−B)=

2

3

,0

∘

<A+B≤90

∘

,A>B then find A and B.

Share

Study later

ANSWER

Given sin(A+B)=1

⇒sin(A+B)=sin90

o

(∵sin90

o

=1)

⇒A+B=90

o

…………(1)

Again, cos(A−B)=

3

/2

⇒cos(A−B)=cos30

o

(∵cos30

o

=

3

/2)

⇒A−B=30

o

…………(2)

Adding (1)+(2)

A+B+A−B=90

o

+30

o

⇒2A=120

o

⇒A=120/2

⇒A=60

o

Putting A=60

o

in equation-(2) we get

A−B=30

o

⇒60

o

−B=30

o

⇒60

o

−30

o

=B

⇒B=30

o

∴A=60

o

;B=30

o

.