Question

1-cos^4a/sin^4a=2cosec^2a-1

Answer 1

Solution:

LHS = (1-cos⁴A)/sin⁴A

= [1² - (cos²A)²]/sin⁴A

= [(1+cos²A)(1-cos²A)]/sin⁴A

/* a²-b² = (a+b)(a-b) */

= [(1+cos²A)sin²A]/(sin²A)²

/* 1-cos²A = sin²A */

= (1+cos²A)/sin²A

= ( 1+1-sin²A)/sin²A

/* cos²A = 1-sin²A */

= (2-sin²A)/sin²A

= 2/sin²A - sin²A/sin²A

= 2cosec²A - 1

/* 1/sin²A = cosec²A */

= RHS

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