Question

If tano= a/b, show that sin²o-cos²o/sin²o+cos²o = a²-b²/a²+b²​

Answer 1

Given :-

• tano= a/b,

To Prove :-

• sin²o-cos²o/sin²o+cos²o = a² - b² / a² + b²

SOLUTION :

→ Here we can also write tan∅ as sin∅ / cos ∅

Therefore,

→ tan ∅ = a / b

→ Sin∅ / cos ∅ = a / b

Hence, The value of sin ∅ is 'a' and cos ∅ is 'b'

Putting the values :-

→ sin²o-cos²o/sin²o+cos²o = a²-b²/a²+b²

→ (a)² - (b)² / (a)² + (b)² = a²-b²/a²+b²

→ a²-b²/a²+b² = a²-b²/a²+b²

→ LHS = RHS

Hence, Proved !