Question

1+tan²A/1+cot²A=tan²A​

Answer 1

Answer:

true

Step-by-step explanation:

we know,

1+tan²A = sec²A

1+cot²A = cosec²A

and 1+tan²A/1+cot²A = sec²A/cosec²A = sin²A/cos²A = tan²A

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Answer 2

S O L U T I O N :

$\underline{\bf{Given\::}}$

1 + tan²A/1 + cot²A = tan²A

$\underline{\bf{Explanation\::}}$

Taking L.H.S :

$\mapsto\tt{\dfrac{1+tan^2 A}{1+cot^2A} }$

$\mapsto\tt{\dfrac{1+\dfrac{sin^2A}{cos^2A} }{1+\dfrac{cos^2A}{sin^2A} } \:\: \underbrace{\sf{\therefore tan \theta = sin\theta /cos\theta \:\:\& \:\: cot \theta = cos\theta /sin\theta }}}$

$\mapsto\tt{\dfrac{\dfrac{cos^2A + sin^2A}{cos^2A} }{\dfrac{sin^A + cos^2A}{sin^2A} }}$

$\mapsto\tt{\dfrac{\cancel{cos^2A + sin^2A}}{cos^2A} \times \dfrac{sin^2A}{\cancel{sin^2A + cos^2A}} }$

$\mapsto\tt{\dfrac{sin^2A}{cos^2A} }$

$\mapsto\bf{tan^2A}$

Thus,

L.H.S = R.H.S

Proved .