if sinQ +cosQ =√3 then prove that tanQ +cosQ =1
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Answer:
SinQ + cosQ = √3
Squaring on both sides we get,
(SinQ + cosQ)² = (√3)²
Sin²Q + cos²Q +2sinQcosQ = 3
1 + 2sinQcosQ = 3
2sinQcosQ = 3-1
SinQ cosQ = 2/2
sinQ cosQ = 1...(1)
tanQ + cotQ = 1
sinQ/ cosQ + cosQ/sinQ = 1
sin²Q + cos²Q /sinQ cosQ = 1
1/sinQ cosQ = 1
sinQcosQ= 1....
thus tanQ+ cotQ = 1
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