Question

6. If in ∆ABC, right-angled at B, sin C = a² - b²/ a² + b² then cosC = ? ​

Answer 1

Step-by-step explanation:

sin(A−B)

=

k

2

(sin

2

A+sin

2

B)

k

2

(sin

2

A−sin

2

B)

by sine formula

or

sinC

sin(A−B)

=

sin

2

A+sin

2

B

sin(A−B)sin(A−B)

or sin(A−B)[

sinC

1

−

sin

2

A+sin

2

B

sinC

]=0

∴ Either sin(A−B)=0 ∴A=B i.e △ is isosceles

or sin

2

A+sin

2

B=sin

2

C or a

2

+b

2

=c

2

∴△ is right angled