Question

(ii) tan^2 A sec^2 (90° – A) – sin^2 A cosec ^2(90° - A) = 1

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Answer 1

Solution:

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i ) sec(90-A) = cosecA

ii) cosec(90-A) = secA

= 1/cosA

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Here,

LHS = tan²Asec²(90-A)-sin²Acosec²(90-A)

= tan²Acosec²A-sin²Asec²A

= tan²Acosec²A - sin²A/cos²A

= tan²Acosec²A - tan²A

/* sinA/cosA = tanA */

= tan²A(cosec²A-1)

/* cosec²A-1 = cot²A */

= tan²Acot²A

/*tanAcotA=1*/

= 1

= RHS