Question

if tan theata =n tan fie and sin theata = m sin fie than, prove that cos² theata = m²-1/n²-1​

Answer 1

Answer:

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.

Step-by-step explanation:

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