Question

Show that : sec^2 $ x cosec^2 $ = sec^2 $ + cosec^2 $​

Answer 1

Answer:

Prove that sec^2 x + cosec^2 x = (sec^2 x)*(cosec*2 x)

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HALA718 eNotes educator | CERTIFIED EDUCATOR

We need to prove that:

sec^2 x +csec^2 x = (sec^2 x)(csec^2 x)

Let us start with the left side:

We know that secx= 1/cosx and csec x = 1/sinx

==> sec^2 x+ cosec^2 x= 1/cos^2 x + 1/sin^2 x

= (sen^2 x + cos^2 x)/(sin^2 x)(cos^2 x)

Now we know that sin^2 x + cos^2 x= 1

==> 1/(sin^2 x)(cos^2 x)= (1/sin^2 x)(1/cos^2 x)

= (sec^2 x)*(csec^2 x)

Answer 2

Answer:

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Step-by-step explanation:

LHS =  cosec^2 theta * sec^2 theta  

=> 1/sin^2 theta * 1/cos^2 theta

=> sin^2 theta + cos^2 theta / sin^2 theta * cos^2 theta

=> 1/cos^2 theta + 1/sin^2 theta

=>sec^2 x + cosec^2 x

hence proved