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if m=tanA+sinA and n=tanA-sinA then what is the value of m^2-n^2

if m=tanA+sinA and
n=tanA-sinA
then what is the value of m^2-n^2

Grade:11

1 Answers

Arun
25763 Points
3 years ago
m2 - n2
(tanA + sinA)2 - (tanA - sinA)2
wkt (a+b)2 - (a-b)=4ab = 4(tanA * sinA)
now RHS 4 root mn
=4√(mn) = 4√((tanA + sinA)(tanA - sinA))
=4√(tan2A - sin2A)
=4√(sin2A/cos2A - sin2A)
=4√((sin2A-sin2A*cos2A)/cos2A)
= 4√sin2A(1-cos2A)/cos2A
=4*sin2A/cosA
=4*sinA*sinA/cosA
=4tanA * sinA

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