Question

tan^A/sec^A+cot^2A/cosec^2A=1

Answer 1

the index two should be given to those trig. ratios for the convenience.

Answer 2

Hey friend,

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Question: $\frac{tan^2A}{sec^2A} + \frac{cot^2A}{cosec^2A} = 1$

Solution:

$=> \frac{tan^2A}{sec^2A} + \frac{cot^2A}{cosec^2A} = 1$

$=> \frac{sin^2A}{cos^2A} \times \frac{1}{sec^2A} + \frac{cos^2A}{sin^2A} \times \frac{1}{cosec^2A}$

$=> \frac{sin^2A}{cos^2A} \times \frac{cos^2A}{1} + \frac{cos^2A}{sin^2A} \times \frac{sin^2A}{1}$

$=> sin^2A + cos^2A$

$=> 1$ {Using identity : sin²Ф + cos²Ф = 1}

$<u><em><strong>LHS = RHS</strong></em></u>$

Hence proved.

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Hope this helped you !!