Question

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Answer 1

Question: If sinA = 8/11, find sec^2A - tan^2A  (ii) cot^2A - cosec^2A + 1

Answer:

Given, sinA = 8/11

Using, cos²A = 1 - sin²A = 1 - (8/11)²

           cos²A = 57/121

        ∴ sec²A = 121/57

tan²A = sin²A/cos²A = (8/11)² / (57/121)

          = 64/57

∴ cot²A = 1/tan²A = 57/64

∴ cosec²A = 1/sin²A = 121/64

(i): sec²A - tan²A = (121/57) - (64/57)

                           = 57/57

                           = 1

(ii): cot²A - cosec²A + 1

                    = 57/64 - 121/64 + 1

                    = (57 - 121 + 64)/64

                    = 0