Question

If tan alpha =n tan beta,sin alpha=m sin beta then prove that cos square alpha=m^2-1/n^2-1​

Answer 1

Answer:

Check the solution below.

Step-by-step explanation:

We have,

tan α = n tan β

⇒ tan β = tan α/n

⇒ cot  β = n/tan α

sin α = m sin β

⇒ sin β = sin α/m

⇒ cosec β = m/sin α

Since

cosec2 β – cot2 β = 1

⇒ m2/sin2 α – n2/tan2 α = 1

⇒  m2/sin2 α – n2 cos2 α/sin2 α = 1

⇒ m2 – n2 cos2 α = sin2 α

⇒ m2 – n2 cos2 α = 1 – cos2 α

⇒ m2 – 1 = (n2 – 1) cos2 α

⇒ cos2 α = (m2 – 1)/(n2 – 1)

Hence proved.