If x =(sec A + sin A) and y = to (sec A- sin A) prove that (2÷x+y)²+(x-y÷2)²=1

If x =(sec A + sin A) and y = to (sec A- sin A) prove that (2÷x+y)²+

1.	If x =(sec A + sin A) and y = to (sec A- sin A) prove that (2÷x+y)²+(x-y÷2)²=1
Answer» Putting Value of X and Y , in LHS we get,\xa0→ (2/x+y)² + (x-y/2)²\xa0→ (2/secA + sinA + secA - sinA)² + (secA + sinA - (secA - sinA)/2)²\xa0→ (2/2secA)² + (secA + sinA - secA + sinA)/2)²\xa0→ 1/sec²A + (2sinA/2)²\xa0[using 1/secA = cosA ]\xa0→ cos²A + sin²A\xa0[ Now , we know that, cos²A + sin²A = 1 ]\xa0Hence,\xa0→ 1 = RHS ( Proved )