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2015-03-24T19:36:41+05:30

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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...



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2015-03-24T20:05:52+05:30
Sec^2Φ=1/cos^2Φ
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
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