Question

If tanα tanβ = 1, then the value of cos(α + β) is

Answer 1

Answer:

0

Step-by-step explanation:

Tan30* tan 60 = 1/root3  *  root3 = 1

so alpha = 30 and beta = 60

And cos( 30+60) = cos90 = 0

Answer 2

If tanα tanβ = 1, then the value of cos (α+β) is equal to 0.

Given:

tanα tanβ = 1

To Find:

cos (α+β)

Solution:

∵ tanαtanβ = 1

→ (sinα sinβ)/(cosα cosβ) = 1

∴ sinα sinβ = cosα cosβ

→By the formula: cos (α+β) = cosαcosβ - sinαsinβ

→cos (α+β) = cosα cosβ - sinα sinβ = sinα sinβ - sinα sinβ = 0

∴ cos (α+β) = 0

Hence, if tanαtanβ = 1, then the value of cos (α+β) is equal to 0.

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