Question

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Answer 1

Answer:

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Step-by-step explanation:

(a.)1-sinA/cosA=cosA/1-sinA

{cross multiplication}

(1-sinA)×(1-sinA)=cosA×cosA

1²-sin²A=cos²A

cos²A=cos²A {as 1-sin²A=cos²A}

(b.)cosA/(1+sinA)+(1+sinA)/cosA=2secA

{taking LCM}

cos²A+(1+sinA)²/cosA(1+sinA)

cos²A+1+sin²A+2 sinA/cosA(1+sinA)

{cos²A+sin²A=1}

1+1+2sinA/cosA(1+sinA)

2+2sinA/cosA(1+sinA)

2(1+sinA)/cosA(1+sinA)

2/cosA

{1/cosA=secA}

2×secA

(c.)(1+cosA)²/(sinA)²=1+cosA/1-cosA

(1+cosA)²/sin²A

{sin²A=1-cos²A}

(1+cosA)²/1-cos²A

{applying a²-b²=(a+b)(a-b)}

(1+cosA)²/(1+cosA)(1-cosA)

1+cosA/1-cosA

(d.)sinA/(1+cosA)+(1+cosA)/sinA=2 cosecA

{taking LCM}

sin²A+(1+cosA)²/sinA(1+cosA)

sin²A+1+cos²A+2cosA/sinA(1+cosA)

{sin²A+cos²A=1}

1+1+2cosA/sinA(1+cosA)

2+2cosA/sinA(1+cosA)

2(1+cosA)/sinA(1+cosA)

2/sinA

{1/sinA=cosecA}

2×cosecA