Question

let A and B are two angle such that sin A + sin B = 1 and cos A + cos B =0 , then value of (36 cos2A+24cos 2B) is equal to
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Answer 1

Suppose A and B are two angles such that A,Bϵ(0,π), and satisfy sinA+sinB=1 and cosA+cosB=0 . Then the value of 12cos2A+4cos2B is ________.

ANSWER

cosA+cosB=0

⇒A+B=π

sinA+sinB=1

⇒sinA=

2

1

=sinB

12[1−2sin

2

A]+4[1−2sin

2

B]

=12[1−

4

2

]+4[1−

4

2

]

=6+4×

2

1

=8