prove that (cosecФ-sinФ)(secФ-cosФ)=1/tanФ+cotФ
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(cosecA-sinA)(secA-cosA)=1/tanA+cotA
(1/sin A - sin A) (1/cosA -cos A = RHS
(1-sin²A /sin A)(1-cos²A/cos A) = Rhs
(cos²A/sinA)(sin²A/cosA) = RHS
cos²Asin²A/ sinA cos A = RHS
sinAcosA(sinAcosA)/sinAcosA = RHS
sinAcosA
Solving RHS
1/tanA+cot A
1/sinA/cosA +cosA/sinA
1/sin²A+cos²A/sinAcosA
1/1/sinAcosA
sinAcosA = LHS
(1/sin A - sin A) (1/cosA -cos A = RHS
(1-sin²A /sin A)(1-cos²A/cos A) = Rhs
(cos²A/sinA)(sin²A/cosA) = RHS
cos²Asin²A/ sinA cos A = RHS
sinAcosA(sinAcosA)/sinAcosA = RHS
sinAcosA
Solving RHS
1/tanA+cot A
1/sinA/cosA +cosA/sinA
1/sin²A+cos²A/sinAcosA
1/1/sinAcosA
sinAcosA = LHS
But LHS=1/tanФ+cotФ
We can solve RHS in questions too
Ok
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