Question

(1 + tan A + sec A)(1 + cot A - cosec A)​

Answer 1

Answer:

2

Step-by-step explanation:

(1 + tan A + sec A)(1 + cot A - cosec A)​

= 1* (1 + cot A - cosec A)​ + tanA*(1 + cot A - cosec A)​+secA(1 + cot A - cosec A)​

= 1 + cot A - cosec A + tanA+tanA.cotA-tanA.cosecA + secA+secA.cotA-secA.cosecA

= 1 + cot A - cosec A + tanA+1 - (sinA/cosA)*(1/sinA) + secA+(1/cosA)(cosA/sinA) - (1/cosA)(1/sinA)

= 2 + cot A - cosec A + tanA  - (1/cosA) + secA + (1/sinA) - secA.cosecA

= 2+cotA-cosecA+tanA - secA + secA + cosecA - secA.cosecA

= 2 + cotA + tanA - (1/sinA)*(1/cosA)

= 2 + (cosA/sinA) + (sinA/cosA) - (1 / sinA.cosA)

= 2 + (cos²A+sin²A)/sinA.cosA - (1 / sinA.cosA)

= 2 + (1 / sinA.cosA) - (1 / sinA.cosA)

= 2