Question

HELP PLS!!!wait what I need to explain my question I think the attachment is enough​

Answer 1

(cosA - sinA + 1)/(cosA + sinA - 1)

rationalising the denominator we get

(cosA + ( 1 - sinA)) (cosA - (1 - sinA))

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(cosA - (1 - sinA))(cosA - (1 - sinA))

cos^2A + (1 - sinA)^2 + 2cosA(1 - sinA)

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cos^2A - (1 - sinA)^2

1 - sin^2A + (1 - sinA)^2 + 2cosA(1 - sinA)

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1 - sin^2A - (1 - sinA)^2

(1+sinA)(1 - sinA) + (1 - sinA)^2 + 2cosA(1 - sinA)

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(1+sinA) ( 1 - sinA) - (1 - sinA)^2

take (1 - sinA) common from numerator and denominator and cancel out (assuming sinA is not 1)

1 + sinA + 1 - sinA + 2 cosA

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1 + sinA - 1 + sinA

2 + 2 cosA

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2 sinA

2(1 + cosA)/ 2 sinA

1/sinA + cosA/sinA

= cosecA + cotA

proved