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LHS;

=> √1/cos²Ф +1/sin²Ф

=> √(sin²Ф+cos²Ф)/(sin²Фcos²Ф)

=> √1/(sin²Фcos²Ф)

=> 1/sinФcosФ

RHS;

=> tanФ+cotФ

=> sinФ/cosФ+cosФ/sinФ

=> (sin²Ф+cos²Ф)/sinФcosФ

=> 1/sinФcosФ

Thus LHS=RHS,

Hence Proved...

=> √1/cos²Ф +1/sin²Ф

=> √(sin²Ф+cos²Ф)/(sin²Фcos²Ф)

=> √1/(sin²Фcos²Ф)

=> 1/sinФcosФ

RHS;

=> tanФ+cotФ

=> sinФ/cosФ+cosФ/sinФ

=> (sin²Ф+cos²Ф)/sinФcosФ

=> 1/sinФcosФ

Thus LHS=RHS,

Hence Proved...

cosec^2Φ=1/sin^2Φ

adding these two we get sin^2Φ +cos^2Φ/sin^2Φ cos^2Φ

therefore the answer is 1/sinΦcosΦ

on the otherhand RHS is tanΦ+cotΦ=sinΦ/cosΦ+cosΦ/sinΦ=1/sinΦcosΦ