Question

prove that 1+tan²A/1+cot²A=(1+tanA/1+cotA )²​

Answer 1

Answer:

L:H:S:

1+tan²A/ 1+ cot² A

= 1+(sin²A/cos²A) /1+( cos²A/sin²A)

=(cos²A+sin ²A) /cos²A/(sin²A +cos²A)/sin²A

= 1/cos²A / 1/sin²A

= tan²A

again,

R:H:S:

(1+tanA/1+cotA)²

={1+( sinA/cosA)/1+ (cosA /sinA)}

= {(cosA +sinA)/cosA/ (sinA+cosA)/sinA}²

= (sinA/cos A)²

= tan²A

L:H:S= R:H:S

hence prooved.

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