Question

5. In a AABC, if ZC = 90°, prove that cosec? A - tan? B = 1.​

Answer 1

Answer:

Given ∠C=90°

To prove that cosec²A - tan²B = 1

Proof:

LHS = cosec²A - tan²B

= cosec²A - tan²(90 - A)          (∵ A and B are complementary angles)

= cosec²A - cot²A                    (∵ cot²A = tan²(90 - A))

= 1 = RHS                                  (∵ cot²A + 1 = cosec²A)

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