if siNΦ+cosΦ=√3 then prove that tanΦ+cotΦ=1
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it is the answer
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Squaring both sides, 1+Sin2Ф=3 ⇒Sin2Ф=2⇒ 2tanФ/(1+tan²Ф)=2 ⇒tan²Ф+1=tanФ⇒tan²Ф-tanФ+1=0
Now, tan²Ф-1/cotФ+1= 0
⇒tanФ-1+cotФ=0 ⇒ tanФ+cotФ=1 (Proved)
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