Question

if sinQ +cosQ =√3 then prove that tanQ +cosQ =1​

Answer 1

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