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

Posted by Vaishnavi Shukla 5 years, 1 month ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 5 years, 1 month ago

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 )

0Thank You

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CBSE > Class 10 > Mathematics