If tan²α = 1 + 2 tan²β (α, β

Home » Aptitude » Trigonometry » Question

If tan²α = 1 + 2 tan²β (α, β are positive acute angles), then √2 cosα – cosβ is equal to

1. 0
2. √2
3. 1
4. - 1

Correct Option: A

tan⊃ α = 1 + 2 tan⊃β
⇒ sec⊃ α – 1 = 1 + 2(sec⊃β – 1)
⇒ sec⊃ α –1 = 2 sec⊃β – 1

⇒		1	=	2
		cos² α		cos² β

⇒ √2 cosα = cosβ
∴ √2 cosα - cosβ = 0