Trigonometry> if cosec theta - sin theta = m and sec th...
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Last Activity: 5 Years ago
Dear student
Cos ^2 ( theta) = m sin ( theta)
Sin ^ 2 ( theta) = n cos ( theta)
Tan ^3 theta = n/m
Using this relation identify sin ^ 2( theta) + cos ^2 ( theta) = 1
Relation thus obtained will be in m and n terms
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Last Activity: 5 Years ago
m = cosecA - sinA
= 1/sinA - sinA
= 1-sin2A / sinA
= cos2A / sinA
m2 = cos4A / sin2A
n = secA - cosA
= 1/cosA - cosA
= 1-cos2A / cosA
sin2A / cosA
n2 = sin4A / cos2A
m2n2= (cos4A / sin2A) * (sin4A / cos2A)
= cos2A sin2A
m2+n2+3 = (cos4A/sin2A) + (sin4A/cos2A) + 3
= sin6A + cos6A / sin2A cos2A + 3
= (sin2A)3 + (cos2A)3 / sin2Acos2A + 3
= (sin2A + cos2A) ( sin4A + cos4A - sin2Acos2A ) / sin2Acos2A + 3
= (sin2A)2 + (cos2A)2 - sin2Acos2A / sin2Acos2A + 3
= (sin2A + cos2A)2 - 2 sin2Acos2A - sin2Acos2A / sin2Acos2A + 3
= 1 - 3 sin2Acos2A + 3 sin2Acos2A / sin2Acos2A
= 1 / sin2Acos2A
m2n2(m2+n2+3) = ( sin2Acos2A ) * ( 1/ sin2Acos2A )
= 1
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