Question

If sin a plus cos a is equal to root two cos a then find the value of cot a

Answer 1

Given

SinA+CosA=√2CosA.....i

Squaring Both Sides:

(SinA+CosA)²=(√2CosA)²

Sin²A+Cos²A+2CosA.SinA=2Cos²A

Sin²A=Cos²A-2CosA.SinA=

Adding Sin²A both sides

2Sin²A=(CosA-SinA)²

√2SinA=CosA-SinA

CosA=SinA(√2+1)

As CosA/SinA=CotA=(√2+1)

Hence,

CotA=√2+1