Question

If tan A =√2-1 , then show that cot A =√2+1?

Answer 1

Answer:

Step-by-step explanation:

tanA=√2-1

or, tanA=(√2-1)(√2+1)/(√2+1)

or, tanA=(2-1)/(√2-1)

or, tanA=1/√2-1

∴, tanA+1/tanA=1/√2-1+√2-1

or, (tan²A+1)/tanA=[1+(√2-1)²]/(√2-1)

or, sec²A/tanA=(1+2-2√2+1)/(√2-1)

or, (1/cos²A)/(sinA/cosA)=(4-2√2)/(√2-1)

or, 1/sinAcosA=(4-2√2)(√2+1)/(√2-1)(√2+1)

or, 1/sinAcosA=(4√2-4+4-2√2)/(2-1)

or, 1/sinAcosA=2√2

or, sinAcosA=1/2√2

or, sinAcosA=√2/2√2.√2

or, sinAcosA=√2/4 (Proved)