Question

Prove that: (sec θ + tan θ)² = (cosec θ +1)/(cosec θ -1)​

Answer 1

Step-by-step explanation:

RHS

cosecA+1/cosecA-1=

cosecA+1/cosecA-1×cosecA+1/cosecA-1

multiplying neumerator and denominator by

cosec A+1 ratiomalising denominator

(cosecA+1)²/cosecA-1×cosecA+1

(cosecA+1)²/cosec²-1²=(cosec+1)²/cot²

1+cot²A=cosec²A

cosecA=1/sinA

(1/sinA+1)²/cot²=(1+sinA/sinA)²/cot²A

cot²A=cos²A/sin²A

=(1+sinA/sinA)²/cos²A/sin²A

=(1+sinA/sinA)²=(1+sin)²/sin²A

=(1+sinA)²/(sinA)²×sin²A/cos²A

=(1+sinA)²/cos²=1+sinA×1+sinA/cosA×CosA

=(secA+tanA)²

you can do this question in 1 more way just try your self maths is just beautiful with wonderful

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