Question

9. If tano + sino = m and tano - sin = n, show that (m2-n2)2 = 16mn.

Answer 1

Answer:

.

Step-by-step explanation:

tano+sino=m. (1)

tano-sino=n. (2)

adding 1 and 2 we get

2tano=m+n. (3)

subtracting (2) from (1)

2sino=m-n. (4)

multiplying (3 )and (4)

m2-n2=4tanosino

m2-n2=4√tan2osin2o

m2-n2=4√tan2o(1-cos2o)

m2-n2 =4√tan2o-tan2ocos2o

m2-n2=4√tan2o-sin20

m2-n2=4√mn

on squaring both side

(m2-n2)2=16mn