Question

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Answer 1

Answer:

4root mn

Step-by-step explanation:

Given,

tan theta+sin theta=m

then theta-sin theta=n

m^2-n^2

putting the vlaues of m and n

(tan theta+sin theta)^2-(tan theta-sin theta)^2

=(tan^2 theta+sin^2 theta+2tan theta*sin theta)-(tan^2 theta+sin^2 theta-2tan theta*sin theta)

= 4 tan θ sin θ….(i)

mn = (tan θ + sin θ)(tan θ – sin θ)

= tan2θ – sin2θ

= (sin2θ/cos2θ) – sin2θ

= sin2θ(sec2θ – 1)

mn = sin2θ tan2θ

Taking square root on both sides,

root mn = sin θ tan θ….(ii)

From (i) and (ii),

m2 – n2 = 4root mn