Prove that cosec4theta-cosec2theta=cot2theta+cot4theta.
Note:2 and 4 are the powers.
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cosec4a-cosec2a=cot2a+cot4a ( let theta=a)
=cosec4a-cot4a=cot2a+cosec2a
now LHS=cosec4a-cot4a
=(cosec2a)2-(cot2a)2
=cosec2a+cot2a )(cosec2a-cot2a). = cosec2a+cot2a
therefore cosec4a-cosec2a=cot4a+cot2a
=cosec4a-cot4a=cot2a+cosec2a
now LHS=cosec4a-cot4a
=(cosec2a)2-(cot2a)2
=cosec2a+cot2a )(cosec2a-cot2a). = cosec2a+cot2a
therefore cosec4a-cosec2a=cot4a+cot2a
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