show that root of sec ² theeta+ Cosec ²theeta=tantheeta +cottheeta
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LHS =root(sec²þ+cose²þ)
root(1/cos²þ+1/sin²þ)
root(sin²þ+cos²þ/sin²þcos²q)
root(1/sin²þcos²q)
root(sec²þcose²þ)
=root((1+tan²þ)(1+cot²þ))
=root(1+tan²þ+cot²q+tan²þcot²q)
=root(1+tan²þ+cot²þ+1) (tan²qcot²þ=1)
=root(tan²þ+cot²þ+2(1))
=root(tan2þ+cot²þ+2(tanþcotþ)
(again identity)
=root(tanþ+cotþ)²
=tanþ+cotþ
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