ORIf cosec θ _ sin θ-m 3 and sec θ-cos θn3 then prove that m4n2 +

1.	ORIf cosec θ _ sin θ-m 3 and sec θ-cos θn3 then prove that m4n2 + m2n4 = 1
Answer» 1/sinθ - sinθ = a^3(1 - sin²θ)/sinθ = a^3cos²θ / sinθ = a^3 similarlysin²θ / cosθ = b^3 thena^4 b^2 + a^2 b^4= [cos²θ/sinθ]^(4/3) [sin²θ / cosθ]^(2/3) + [cos²θ/sinθ]^(2/3) [sin²θ / cosθ]^(4/3) = (cosθ)^(8/3) / (cosθ)^(2/3) + (sinθ)^(8/3) / (sinθ)^(2/3) = cos²θ + sin²θ= 1

ORIf cosec θ _ sin θ-m 3 and sec θ-cos θn3 then prove that m4n2 + m2n4 = 1

Answer»

1/sinθ - sinθ = a^3(1 - sin²θ)/sinθ = a^3cos²θ / sinθ = a^3

similarlysin²θ / cosθ = b^3

thena^4 b^2 + a^2 b^4= [cos²θ/sinθ]^(4/3) [sin²θ / cosθ]^(2/3) + [cos²θ/sinθ]^(2/3) [sin²θ / cosθ]^(4/3)

= (cosθ)^(8/3) / (cosθ)^(2/3) + (sinθ)^(8/3) / (sinθ)^(2/3)

= cos²θ + sin²θ= 1