Question

If x = sec A + sin A and y = sec A - sin A, prove that
= sec A - sin A, prove that (2/x+y)^2 + (x-y/2)^2=1​

Answer 1

Correct Question :--- If x = sec A + sin A and y = sec A - sin A, prove that (2/x+y)²+ (x-y/2)² = 1

Solution :----

Putting Value of X and Y , in LHS we get,

→ (2/x+y)² + (x-y/2)²

→ (2/secA + sinA + secA - sinA)² + (secA + sinA - (secA - sinA)/2)²

→ (2/2secA)² + (secA + sinA - secA + sinA)/2)²

→ 1/sec²A + (2sinA/2)²

[using 1/secA = cosA ]

→ cos²A + sin²A

[ Now , we know that, cos²A + sin²A = 1 ]

Hence,

→ 1 = RHS ( Proved )

Answer 2

Putting Value of X and Y , in LHS we get,

→ (2/x+y)² + (x-y/2)²

→ (2/secA + sinA + secA - sinA)² + (secA + sinA - (secA - sinA)/2)²

→ (2/2secA)² + (secA + sinA - secA + sinA)/2)²

→ 1/sec²A + (2sinA/2)²

[using 1/secA = cosA ]

→ cos²A + sin²A

[ Now , we know that, cos²A + sin²A = 1 ]

Hence,

→ 1 = RHS ( Proved )