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Prove `: cot^(2) theta-tan^(2)theta=cosec^(2)theta-sec^(2)theta` |
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Answer» Proof: `LHS =cot^(2) theta-tan^(2)theta` `=(cosec^(2)theta-1)-(sec^(2)theta-1)…{:[(cosec^(2)theta=1+cot^(2)theta),(sec^(2)theta=1+tan^(2)theta)]:}` `=cosec^(2) theta-1-sec^(2)theta+1` `=cosec^(2) theta-sec^(2) theta` `=RHS` `:.cot^(2) theta-tan^(2)theta=cosec^(2)theta-sec^(2)theta`. |
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