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If sin θ = mnm+n; Find the value ...

If sin θ = mnm+n; Find the value of 1 + tan2θ

A.

(m2+n2)m+n

B.

(m2+n2+2mn)4mn

C.

2(m2+n2+mn)m+n

D.

(m2+n2+mn)m+n

Correct answer is B

(m+n)2=(mn)2+x2

m2+2mn+n2=m22mn+n2+x2

x2=4mn

x=4mn=2mn

1 + tan2θ = sec2θ

= 1cos2θ

cosθ=2mn(m+n)

1cosθ=(m+n)2mn

sec2θ=(m+n)24mn

= (m2+n2+2mn)4mn