Question

if
n Sin A=m Cos A

show that
m sin A- n CosA/ =m^2-n^2/
m Sin A + n CosA m^2+n^2

Answer 1

Answer:

Given cosA−sinA=m and cosA+sinA=n

want to show :

m

2

+n

2

m

2

−n

2

=−2sinAcosA=

tanA+cotA

−2

proof :- firstly observe that

tanA+cotA

−2

=

cosA

sinA

+

sinA

cosA

−2

=

sin

2

A+cos

2

A

2sinAcosA

=−2sinAcosA

m

2

−n

2

=(cosA−sinA)

2

−(cosA+sinA)

2

=(cos

2

A+sin

2

A−2cosAsinA)−(cos

2

A+sin

2

A=2cosAsinA)

=−4cosAsinA

m

2

−n

2

=(cosA−sinA)

2

−(cosA+sinA)

2

=(cos

2

A+sin

2

A−2cosAsinA)−(cos

2

A+sin

2

A=2cosAsinA)

=2(cos

2

A+sin

2

A)

=2

thus ,

m

2

+n

2

m

2

−n

2

=−2cosAsinA=

tanA+cotA

−2

please Bhai tum mera answer ko brainliest kar do please hmm tumko aur thanks as return me