Question

Please prove this :-​

Answer 1

Answer:

sec² A + cosec² A/sec A. cosec A = sec A. cosec A

L.H.S. :-

sec² A + cosec² A/sec A. cosec A

1/cos²A + 1/sin²A / sec A. cosec A

sin²A+cos²A/cos²A.sin²A / 1/cosA. 1/sinA

⇒ sin²A+cos²A/cos²A.sin²A X cosA.sinA        {Here we did reciprocal of the term, so as it was getting devided; after reciprocal it multiplies}

sin²A+cos²A/cosA.sinA               {Here the bold one in the upper step got

                                                           divided with cosA.sinA}

As we know, sin²A+cos²A = 1

So, we get:-

1/cosA.sinA

= secA.cosecA   = R.H.S            {reciprocal of 1/cosA is secA and of 1/sinA is

                                                           cosecA}

HENCE PROVED

Step-by-step explanation:

Hope it helps you buddy :)