Question

If sin 0 + cos 0 = V3, then prove that tan 0 + cot 0 =1​

Answer 1

Step-by-step explanation:

theta is taken as A.

=> sinA+ cosA= √3

=> (sinA+ cosA)^2 = (√3)^2

=> sin^2 A+ cos^2 A + 2sinAcosA = 3

=> 1 + 2sinAcosA = 3 (as sin^2 A + cos^2 A = 1)

=> 2sinAcosA = 2

=> sinAcosA = 1

to prove : tanA + cotA = 1

tanA + cotA

= sinA + cosA

cosA sinA

= sin^2 A + cos^2 A

sinAcosA

= 1

as sin^2 A + cos^2 A = 1 and sinAcosA = 1 (as proved above)

Hence, proved.